math_geom.c

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/*
 * ***** BEGIN GPL LICENSE BLOCK *****
 *
 * This program is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public License
 * as published by the Free Software Foundation; either version 2
 * of the License, or (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software Foundation,
 * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
 *
 * The Original Code is Copyright (C) 2001-2002 by NaN Holding BV.
 * All rights reserved.
 
 * The Original Code is: some of this file.
 *
 * ***** END GPL LICENSE BLOCK *****
 * */

#include "MEM_guardedalloc.h"

#include "BLI_math.h"
#include "BLI_memarena.h"
#include "BLI_utildefines.h"

/********************************** Polygons *********************************/

void cent_tri_v3(float cent[3], const float v1[3], const float v2[3], const float v3[3])
{
    cent[0]= 0.33333f*(v1[0]+v2[0]+v3[0]);
    cent[1]= 0.33333f*(v1[1]+v2[1]+v3[1]);
    cent[2]= 0.33333f*(v1[2]+v2[2]+v3[2]);
}

void cent_quad_v3(float cent[3], const float v1[3], const float v2[3], const float v3[3], const float v4[3])
{
    cent[0]= 0.25f*(v1[0]+v2[0]+v3[0]+v4[0]);
    cent[1]= 0.25f*(v1[1]+v2[1]+v3[1]+v4[1]);
    cent[2]= 0.25f*(v1[2]+v2[2]+v3[2]+v4[2]);
}

float normal_tri_v3(float n[3], const float v1[3], const float v2[3], const float v3[3])
{
    float n1[3],n2[3];

    n1[0]= v1[0]-v2[0];
    n2[0]= v2[0]-v3[0];
    n1[1]= v1[1]-v2[1];
    n2[1]= v2[1]-v3[1];
    n1[2]= v1[2]-v2[2];
    n2[2]= v2[2]-v3[2];
    n[0]= n1[1]*n2[2]-n1[2]*n2[1];
    n[1]= n1[2]*n2[0]-n1[0]*n2[2];
    n[2]= n1[0]*n2[1]-n1[1]*n2[0];

    return normalize_v3(n);
}

float normal_quad_v3(float n[3], const float v1[3], const float v2[3], const float v3[3], const float v4[3])
{
    /* real cross! */
    float n1[3],n2[3];

    n1[0]= v1[0]-v3[0];
    n1[1]= v1[1]-v3[1];
    n1[2]= v1[2]-v3[2];

    n2[0]= v2[0]-v4[0];
    n2[1]= v2[1]-v4[1];
    n2[2]= v2[2]-v4[2];

    n[0]= n1[1]*n2[2]-n1[2]*n2[1];
    n[1]= n1[2]*n2[0]-n1[0]*n2[2];
    n[2]= n1[0]*n2[1]-n1[1]*n2[0];

    return normalize_v3(n);
}

float area_tri_v2(const float v1[2], const float v2[2], const float v3[2])
{
    return 0.5f * fabsf((v1[0]-v2[0])*(v2[1]-v3[1]) + (v1[1]-v2[1])*(v3[0]-v2[0]));
}

float area_tri_signed_v2(const float v1[2], const float v2[2], const float v3[2])
{
    return 0.5f * ((v1[0]-v2[0])*(v2[1]-v3[1]) + (v1[1]-v2[1])*(v3[0]-v2[0]));
}

float area_quad_v3(const float v1[3], const float v2[3], const float v3[3], const float v4[3])  /* only convex Quadrilaterals */
{
    float len, vec1[3], vec2[3], n[3];

    sub_v3_v3v3(vec1, v2, v1);
    sub_v3_v3v3(vec2, v4, v1);
    cross_v3_v3v3(n, vec1, vec2);
    len= normalize_v3(n);

    sub_v3_v3v3(vec1, v4, v3);
    sub_v3_v3v3(vec2, v2, v3);
    cross_v3_v3v3(n, vec1, vec2);
    len+= normalize_v3(n);

    return (len/2.0f);
}

float area_tri_v3(const float v1[3], const float v2[3], const float v3[3])  /* Triangles */
{
    float len, vec1[3], vec2[3], n[3];

    sub_v3_v3v3(vec1, v3, v2);
    sub_v3_v3v3(vec2, v1, v2);
    cross_v3_v3v3(n, vec1, vec2);
    len= normalize_v3(n);

    return (len/2.0f);
}

float area_poly_v3(int nr, float verts[][3], const float normal[3])
{
    float x, y, z, area, max;
    float *cur, *prev;
    int a, px=0, py=1;

    /* first: find dominant axis: 0==X, 1==Y, 2==Z
     * don't use 'axis_dominant_v3()' because we need max axis too */
    x= fabsf(normal[0]);
    y= fabsf(normal[1]);
    z= fabsf(normal[2]);
    max = MAX3(x, y, z);
    if(max==y) py=2;
    else if(max==x) {
        px=1; 
        py= 2;
    }

    /* The Trapezium Area Rule */
    prev= verts[nr-1];
    cur= verts[0];
    area= 0;
    for(a=0; a<nr; a++) {
        area+= (cur[px]-prev[px])*(cur[py]+prev[py]);
        prev= verts[a];
        cur= verts[a+1];
    }

    return fabsf(0.5f * area / max);
}

/********************************* Distance **********************************/

/* distance v1 to line v2-v3 */
/* using Hesse formula, NO LINE PIECE! */
float dist_to_line_v2(const float v1[2], const float v2[2], const float v3[2])
{
    float a[2],deler;

    a[0]= v2[1]-v3[1];
    a[1]= v3[0]-v2[0];
    deler= (float)sqrt(a[0]*a[0]+a[1]*a[1]);
    if(deler== 0.0f) return 0;

    return fabsf((v1[0]-v2[0])*a[0]+(v1[1]-v2[1])*a[1])/deler;

}

/* distance v1 to line-piece v2-v3 */
float dist_to_line_segment_v2(const float v1[2], const float v2[2], const float v3[2])
{
    float labda, rc[2], pt[2], len;
    
    rc[0]= v3[0]-v2[0];
    rc[1]= v3[1]-v2[1];
    len= rc[0]*rc[0]+ rc[1]*rc[1];
    if(len==0.0f) {
        rc[0]= v1[0]-v2[0];
        rc[1]= v1[1]-v2[1];
        return (float)(sqrt(rc[0]*rc[0]+ rc[1]*rc[1]));
    }
    
    labda= (rc[0]*(v1[0]-v2[0]) + rc[1]*(v1[1]-v2[1]))/len;
    if(labda <= 0.0f) {
        pt[0]= v2[0];
        pt[1]= v2[1];
    }
    else if(labda >= 1.0f) {
        pt[0]= v3[0];
        pt[1]= v3[1];
    }
    else {
        pt[0]= labda*rc[0]+v2[0];
        pt[1]= labda*rc[1]+v2[1];
    }

    rc[0]= pt[0]-v1[0];
    rc[1]= pt[1]-v1[1];
    return sqrtf(rc[0]*rc[0]+ rc[1]*rc[1]);
}

/* point closest to v1 on line v2-v3 in 2D */
void closest_to_line_segment_v2(float close_r[2], const float p[2], const float l1[2], const float l2[2])
{
    float lambda, cp[2];

    lambda= closest_to_line_v2(cp,p, l1, l2);

    if(lambda <= 0.0f)
        copy_v2_v2(close_r, l1);
    else if(lambda >= 1.0f)
        copy_v2_v2(close_r, l2);
    else
        copy_v2_v2(close_r, cp);
}

/* point closest to v1 on line v2-v3 in 3D */
void closest_to_line_segment_v3(float close_r[3], const float v1[3], const float v2[3], const float v3[3])
{
    float lambda, cp[3];

    lambda= closest_to_line_v3(cp,v1, v2, v3);

    if(lambda <= 0.0f)
        copy_v3_v3(close_r, v2);
    else if(lambda >= 1.0f)
        copy_v3_v3(close_r, v3);
    else
        copy_v3_v3(close_r, cp);
}

/* find the closest point on a plane to another point and store it in close_r
 * close_r:       return coordinate
 * plane_co:      a point on the plane
 * plane_no_unit: the plane's normal, and d is the last number in the plane equation 0 = ax + by + cz + d
 * pt:            the point that you want the nearest of
 */

// const float norm[3], const float coord[3], const float point[3], float dst_r[3]
void closest_to_plane_v3(float close_r[3], const float plane_co[3], const float plane_no_unit[3], const float pt[3])
{
    float temp[3];
    float dotprod;

    sub_v3_v3v3(temp, pt, plane_co);
    dotprod= dot_v3v3(temp, plane_no_unit);

    close_r[0] = pt[0] - (plane_no_unit[0] * dotprod);
    close_r[1] = pt[1] - (plane_no_unit[1] * dotprod);
    close_r[2] = pt[2] - (plane_no_unit[2] * dotprod);
}

/* signed distance from the point to the plane in 3D */
float dist_to_plane_normalized_v3(const float p[3], const float plane_co[3], const float plane_no_unit[3])
{
    float plane_co_other[3];

    add_v3_v3v3(plane_co_other, plane_co, plane_no_unit);

    return line_point_factor_v3(p, plane_co, plane_co_other);
}

float dist_to_plane_v3(const float p[3], const float plane_co[3], const float plane_no[3])
{
    float plane_no_unit[3];
    float plane_co_other[3];

    normalize_v3_v3(plane_no_unit, plane_no);
    add_v3_v3v3(plane_co_other, plane_co, plane_no_unit);

    return line_point_factor_v3(p, plane_co, plane_co_other);
}

/* distance v1 to line-piece v2-v3 in 3D */
float dist_to_line_segment_v3(const float v1[3], const float v2[3], const float v3[3])
{
    float closest[3];

    closest_to_line_segment_v3(closest, v1, v2, v3);

    return len_v3v3(closest, v1);
}

/******************************* Intersection ********************************/

/* intersect Line-Line, shorts */
int isect_line_line_v2_int(const int v1[2], const int v2[2], const int v3[2], const int v4[2])
{
    float div, labda, mu;
    
    div= (float)((v2[0]-v1[0])*(v4[1]-v3[1])-(v2[1]-v1[1])*(v4[0]-v3[0]));
    if(div==0.0f) return ISECT_LINE_LINE_COLINEAR;
    
    labda= ((float)(v1[1]-v3[1])*(v4[0]-v3[0])-(v1[0]-v3[0])*(v4[1]-v3[1]))/div;
    
    mu= ((float)(v1[1]-v3[1])*(v2[0]-v1[0])-(v1[0]-v3[0])*(v2[1]-v1[1]))/div;
    
    if(labda>=0.0f && labda<=1.0f && mu>=0.0f && mu<=1.0f) {
        if(labda==0.0f || labda==1.0f || mu==0.0f || mu==1.0f) return ISECT_LINE_LINE_EXACT;
        return ISECT_LINE_LINE_CROSS;
    }
    return ISECT_LINE_LINE_NONE;
}

/* intersect Line-Line, floats */
int isect_line_line_v2(const float v1[2], const float v2[2], const float v3[2], const float v4[2])
{
    float div, labda, mu;
    
    div= (v2[0]-v1[0])*(v4[1]-v3[1])-(v2[1]-v1[1])*(v4[0]-v3[0]);
    if(div==0.0f) return ISECT_LINE_LINE_COLINEAR;
    
    labda= ((float)(v1[1]-v3[1])*(v4[0]-v3[0])-(v1[0]-v3[0])*(v4[1]-v3[1]))/div;
    
    mu= ((float)(v1[1]-v3[1])*(v2[0]-v1[0])-(v1[0]-v3[0])*(v2[1]-v1[1]))/div;
    
    if(labda>=0.0f && labda<=1.0f && mu>=0.0f && mu<=1.0f) {
        if(labda==0.0f || labda==1.0f || mu==0.0f || mu==1.0f) return ISECT_LINE_LINE_EXACT;
        return ISECT_LINE_LINE_CROSS;
    }
    return ISECT_LINE_LINE_NONE;
}

/* get intersection point of two 2D segments and return intersection type:
    -1: colliniar
     1: intersection */
int isect_seg_seg_v2_point(const float v1[2], const float v2[2], const float v3[2], const float v4[2], float vi[2])
{
    float a1, a2, b1, b2, c1, c2, d;
    float u, v;
    const float eps= 0.000001f;

    a1= v2[0]-v1[0];
    b1= v4[0]-v3[0];
    c1= v1[0]-v4[0];

    a2= v2[1]-v1[1];
    b2= v4[1]-v3[1];
    c2= v1[1]-v4[1];

    d= a1*b2-a2*b1;

    if(d==0) {
        if(a1*c2-a2*c1==0.0f && b1*c2-b2*c1==0.0f) { /* equal lines */
            float a[2], b[2], c[2];
            float u2;

            if(len_v2v2(v1, v2)==0.0f) {
                if(len_v2v2(v3, v4)>eps) {
                    /* use non-point segment as basis */
                    SWAP(const float *, v1, v3);
                    SWAP(const float *, v2, v4);
                } else { /* both of segments are points */
                    if(equals_v2v2(v1, v3)) { /* points are equal */
                        copy_v2_v2(vi, v1);
                        return 1;
                    }

                    /* two different points */
                    return -1;
                }
            }

            sub_v2_v2v2(a, v3, v1);
            sub_v2_v2v2(b, v2, v1);
            sub_v2_v2v2(c, v2, v1);
            u= dot_v2v2(a, b) / dot_v2v2(c, c);

            sub_v2_v2v2(a, v4, v1);
            u2= dot_v2v2(a, b) / dot_v2v2(c, c);

            if(u>u2) SWAP(float, u, u2);

            if(u>1.0f+eps || u2<-eps) return -1; /* non-ovlerlapping segments */
            else if(maxf(0.0f, u) == minf(1.0f, u2)){ /* one common point: can return result */
                interp_v2_v2v2(vi, v1, v2, maxf(0, u));
                return 1;
            }
        }

        /* lines are colliniar */
        return -1;
    }

    u= (c2*b1-b2*c1)/d;
    v= (c1*a2-a1*c2)/d;

    if(u>=-eps && u<=1.0f+eps && v>=-eps && v<=1.0f+eps) { /* intersection */
        interp_v2_v2v2(vi, v1, v2, u);
        return 1;
    }

    /* out of segment intersection */
    return -1;
}

int isect_line_sphere_v3(const float l1[3], const float l2[3],
                         const float sp[3], const float r,
                         float r_p1[3], float r_p2[3])
{
    /* l1:         coordinates (point of line)
     * l2:         coordinates (point of line)
     * sp, r:      coordinates and radius (sphere)
     * r_p1, r_p2: return intersection coordinates
     */


    /* adapted for use in blender by Campbell Barton - 2011
     *
     * atelier iebele abel - 2001
     * atelier@iebele.nl
     * http://www.iebele.nl
     *
     * sphere_line_intersection function adapted from:
     * http://astronomy.swin.edu.au/pbourke/geometry/sphereline
     * Paul Bourke pbourke@swin.edu.au
     */

    const float ldir[3]= {
        l2[0] - l1[0],
        l2[1] - l1[1],
        l2[2] - l1[2]
    };

    const float a= dot_v3v3(ldir, ldir);

    const float b= 2.0f *
            (ldir[0] * (l1[0] - sp[0]) +
             ldir[1] * (l1[1] - sp[1]) +
             ldir[2] * (l1[2] - sp[2]));

    const float c=
            dot_v3v3(sp, sp) +
            dot_v3v3(l1, l1) -
            (2.0f * dot_v3v3(sp, l1)) -
            (r * r);

    const float i = b * b - 4.0f * a * c;

    float mu;

    if (i < 0.0f) {
        /* no intersections */
        return 0;
    }
    else if (i == 0.0f) {
        /* one intersection */
        mu = -b / (2.0f * a);
        madd_v3_v3v3fl(r_p1, l1, ldir, mu);
        return 1;
    }
    else if (i > 0.0f) {
        const float i_sqrt= sqrt(i); /* avoid calc twice */

        /* first intersection */
        mu = (-b + i_sqrt) / (2.0f * a);
        madd_v3_v3v3fl(r_p1, l1, ldir, mu);

        /* second intersection */
        mu = (-b - i_sqrt) / (2.0f * a);
        madd_v3_v3v3fl(r_p2, l1, ldir, mu);
        return 2;
    }
    else {
        /* math domain error - nan */
        return -1;
    }
}

/* keep in sync with isect_line_sphere_v3 */
int isect_line_sphere_v2(const float l1[2], const float l2[2],
                         const float sp[2], const float r,
                         float r_p1[2], float r_p2[2])
{
    const float ldir[2]= {
        l2[0] - l1[0],
        l2[1] - l1[1]
    };

    const float a= dot_v2v2(ldir, ldir);

    const float b= 2.0f *
            (ldir[0] * (l1[0] - sp[0]) +
             ldir[1] * (l1[1] - sp[1]));

    const float c=
            dot_v2v2(sp, sp) +
            dot_v2v2(l1, l1) -
            (2.0f * dot_v2v2(sp, l1)) -
            (r * r);

    const float i = b * b - 4.0f * a * c;

    float mu;

    if (i < 0.0f) {
        /* no intersections */
        return 0;
    }
    else if (i == 0.0f) {
        /* one intersection */
        mu = -b / (2.0f * a);
        madd_v2_v2v2fl(r_p1, l1, ldir, mu);
        return 1;
    }
    else if (i > 0.0f) {
        const float i_sqrt= sqrt(i); /* avoid calc twice */

        /* first intersection */
        mu = (-b + i_sqrt) / (2.0f * a);
        madd_v2_v2v2fl(r_p1, l1, ldir, mu);

        /* second intersection */
        mu = (-b - i_sqrt) / (2.0f * a);
        madd_v2_v2v2fl(r_p2, l1, ldir, mu);
        return 2;
    }
    else {
        /* math domain error - nan */
        return -1;
    }
}

/*
-1: colliniar
 1: intersection

*/
static short IsectLLPt2Df(const float x0, const float y0, const float x1, const float y1,
                     const float x2, const float y2, const float x3, const float y3, float *xi,float *yi)

{
    /*
    this function computes the intersection of the sent lines
    and returns the intersection point, note that the function assumes
    the lines intersect. the function can handle vertical as well
    as horizontal lines. note the function isn't very clever, it simply
    applies the math, but we don't need speed since this is a
    pre-processing step
    */
    float c1,c2, // constants of linear equations
    det_inv,  // the inverse of the determinant of the coefficient
    m1,m2;    // the slopes of each line
    /*
    compute slopes, note the cludge for infinity, however, this will
    be close enough
    */
    if (fabs(x1-x0) > 0.000001)
        m1 = (y1-y0) / (x1-x0);
    else
        return -1; /*m1 = (float) 1e+10;*/   // close enough to infinity

    if (fabs(x3-x2) > 0.000001)
        m2 = (y3-y2) / (x3-x2);
    else
        return -1; /*m2 = (float) 1e+10;*/   // close enough to infinity

    if (fabs(m1-m2) < 0.000001)
        return -1; /* parallel lines */
    
// compute constants

    c1 = (y0-m1*x0);
    c2 = (y2-m2*x2);

// compute the inverse of the determinate

    det_inv = 1.0f / (-m1 + m2);

// use Kramers rule to compute xi and yi

    *xi= ((-c2 + c1) *det_inv);
    *yi= ((m2*c1 - m1*c2) *det_inv);
    
    return 1; 
} // end Intersect_Lines

/* point in tri */

int isect_point_tri_v2(const float pt[2], const float v1[2], const float v2[2], const float v3[2])
{
    if (line_point_side_v2(v1,v2,pt)>=0.0f) {
        if (line_point_side_v2(v2,v3,pt)>=0.0f) {
            if (line_point_side_v2(v3,v1,pt)>=0.0f) {
                return 1;
            }
        }
    } else {
        if (! (line_point_side_v2(v2,v3,pt)>=0.0f)) {
            if (! (line_point_side_v2(v3,v1,pt)>=0.0f)) {
                return -1;
            }
        }
    }
    
    return 0;
}
/* point in quad - only convex quads */
int isect_point_quad_v2(const float pt[2], const float v1[2], const float v2[2], const float v3[2], const float v4[2])
{
    if (line_point_side_v2(v1,v2,pt)>=0.0f) {
        if (line_point_side_v2(v2,v3,pt)>=0.0f) {
            if (line_point_side_v2(v3,v4,pt)>=0.0f) {
                if (line_point_side_v2(v4,v1,pt)>=0.0f) {
                    return 1;
                }
            }
        }
    } else {
        if (! (line_point_side_v2(v2,v3,pt)>=0.0f)) {
            if (! (line_point_side_v2(v3,v4,pt)>=0.0f)) {
                if (! (line_point_side_v2(v4,v1,pt)>=0.0f)) {
                    return -1;
                }
            }
        }
    }
    
    return 0;
}

/* moved from effect.c
   test if the line starting at p1 ending at p2 intersects the triangle v0..v2
   return non zero if it does 
*/
int isect_line_tri_v3(const float p1[3], const float p2[3],
                      const float v0[3], const float v1[3], const float v2[3],
                      float *r_lambda, float r_uv[2])
{

    float p[3], s[3], d[3], e1[3], e2[3], q[3];
    float a, f, u, v;
    
    sub_v3_v3v3(e1, v1, v0);
    sub_v3_v3v3(e2, v2, v0);
    sub_v3_v3v3(d, p2, p1);
    
    cross_v3_v3v3(p, d, e2);
    a = dot_v3v3(e1, p);
    if ((a > -0.000001f) && (a < 0.000001f)) return 0;
    f = 1.0f/a;
    
    sub_v3_v3v3(s, p1, v0);
    
    u = f * dot_v3v3(s, p);
    if ((u < 0.0f)||(u > 1.0f)) return 0;
    
    cross_v3_v3v3(q, s, e1);
    
    v = f * dot_v3v3(d, q);
    if ((v < 0.0f)||((u + v) > 1.0f)) return 0;

    *r_lambda = f * dot_v3v3(e2, q);
    if ((*r_lambda < 0.0f)||(*r_lambda > 1.0f)) return 0;

    if(r_uv) {
        r_uv[0]= u;
        r_uv[1]= v;
    }
    
    return 1;
}
/* moved from effect.c
   test if the ray starting at p1 going in d direction intersects the triangle v0..v2
   return non zero if it does 
*/
int isect_ray_tri_v3(const float p1[3], const float d[3],
                     const float v0[3], const float v1[3], const float v2[3],
                     float *r_lambda, float r_uv[2])
{
    float p[3], s[3], e1[3], e2[3], q[3];
    float a, f, u, v;
    
    sub_v3_v3v3(e1, v1, v0);
    sub_v3_v3v3(e2, v2, v0);
    
    cross_v3_v3v3(p, d, e2);
    a = dot_v3v3(e1, p);
    /* note: these values were 0.000001 in 2.4x but for projection snapping on
     * a human head (1BU==1m), subsurf level 2, this gave many errors - campbell */
    if ((a > -0.00000001f) && (a < 0.00000001f)) return 0;
    f = 1.0f/a;
    
    sub_v3_v3v3(s, p1, v0);
    
    u = f * dot_v3v3(s, p);
    if ((u < 0.0f)||(u > 1.0f)) return 0;

    cross_v3_v3v3(q, s, e1);
    
    v = f * dot_v3v3(d, q);
    if ((v < 0.0f)||((u + v) > 1.0f)) return 0;

    *r_lambda = f * dot_v3v3(e2, q);
    if ((*r_lambda < 0.0f)) return 0;

    if(r_uv) {
        r_uv[0]= u;
        r_uv[1]= v;
    }
    
    return 1;
}

int isect_ray_plane_v3(const float p1[3], const float d[3],
                       const float v0[3], const float v1[3], const float v2[3],
                       float *r_lambda, const int clip)
{
    float p[3], s[3], e1[3], e2[3], q[3];
    float a, f;
    /* float  u, v; */ /*UNUSED*/

    sub_v3_v3v3(e1, v1, v0);
    sub_v3_v3v3(e2, v2, v0);
    
    cross_v3_v3v3(p, d, e2);
    a = dot_v3v3(e1, p);
    /* note: these values were 0.000001 in 2.4x but for projection snapping on
     * a human head (1BU==1m), subsurf level 2, this gave many errors - campbell */
    if ((a > -0.00000001f) && (a < 0.00000001f)) return 0;
    f = 1.0f/a;
    
    sub_v3_v3v3(s, p1, v0);
    
    /* u = f * dot_v3v3(s, p); */ /*UNUSED*/

    cross_v3_v3v3(q, s, e1);
    
    /* v = f * dot_v3v3(d, q); */ /*UNUSED*/

    *r_lambda = f * dot_v3v3(e2, q);
    if (clip && (*r_lambda < 0.0f)) return 0;

    return 1;
}

int isect_ray_tri_epsilon_v3(const float p1[3], const float d[3],
                             const float v0[3], const float v1[3], const float v2[3],
                             float *r_lambda, float uv[2], const float epsilon)
{
    float p[3], s[3], e1[3], e2[3], q[3];
    float a, f, u, v;

    sub_v3_v3v3(e1, v1, v0);
    sub_v3_v3v3(e2, v2, v0);

    cross_v3_v3v3(p, d, e2);
    a = dot_v3v3(e1, p);
    if (a == 0.0f) return 0;
    f = 1.0f/a;

    sub_v3_v3v3(s, p1, v0);

    u = f * dot_v3v3(s, p);
    if ((u < -epsilon)||(u > 1.0f+epsilon)) return 0;

    cross_v3_v3v3(q, s, e1);

    v = f * dot_v3v3(d, q);
    if ((v < -epsilon)||((u + v) > 1.0f+epsilon)) return 0;

    *r_lambda = f * dot_v3v3(e2, q);
    if ((*r_lambda < 0.0f)) return 0;

    if(uv) {
        uv[0]= u;
        uv[1]= v;
    }

    return 1;
}

int isect_ray_tri_threshold_v3(const float p1[3], const float d[3],
                               const float v0[3], const float v1[3], const float v2[3],
                               float *r_lambda, float r_uv[2], const float threshold)
{
    float p[3], s[3], e1[3], e2[3], q[3];
    float a, f, u, v;
    float du = 0, dv = 0;
    
    sub_v3_v3v3(e1, v1, v0);
    sub_v3_v3v3(e2, v2, v0);
    
    cross_v3_v3v3(p, d, e2);
    a = dot_v3v3(e1, p);
    if ((a > -0.000001f) && (a < 0.000001f)) return 0;
    f = 1.0f/a;
    
    sub_v3_v3v3(s, p1, v0);
    
    cross_v3_v3v3(q, s, e1);
    *r_lambda = f * dot_v3v3(e2, q);
    if ((*r_lambda < 0.0f)) return 0;
    
    u = f * dot_v3v3(s, p);
    v = f * dot_v3v3(d, q);
    
    if (u < 0) du = u;
    if (u > 1) du = u - 1;
    if (v < 0) dv = v;
    if (v > 1) dv = v - 1;
    if (u > 0 && v > 0 && u + v > 1)
    {
        float t = u + v - 1;
        du = u - t/2;
        dv = v - t/2;
    }

    mul_v3_fl(e1, du);
    mul_v3_fl(e2, dv);
    
    if (dot_v3v3(e1, e1) + dot_v3v3(e2, e2) > threshold * threshold)
    {
        return 0;
    }

    if(r_uv) {
        r_uv[0]= u;
        r_uv[1]= v;
    }
    
    return 1;
}

int isect_line_plane_v3(float out[3], const float l1[3], const float l2[3], const float plane_co[3], const float plane_no[3], const short no_flip)
{
    float l_vec[3]; /* l1 -> l2 normalized vector */
    float p_no[3]; /* 'plane_no' normalized */
    float dot;

    sub_v3_v3v3(l_vec, l2, l1);

    normalize_v3(l_vec);
    normalize_v3_v3(p_no, plane_no);

    dot= dot_v3v3(l_vec, p_no);
    if(dot == 0.0f) {
        return 0;
    }
    else {
        float l1_plane[3]; /* line point aligned with the plane */
        float dist; /* 'plane_no' aligned distance to the 'plane_co' */

        /* for pradictable flipping since the plane is only used to
         * define a direction, ignore its flipping and aligned with 'l_vec' */
        if(dot < 0.0f) {
            dot= -dot;
            negate_v3(p_no);
        }

        add_v3_v3v3(l1_plane, l1, p_no);

        dist = line_point_factor_v3(plane_co, l1, l1_plane);

        /* treat line like a ray, when 'no_flip' is set */
        if(no_flip && dist < 0.0f) {
            dist= -dist;
        }

        mul_v3_fl(l_vec, dist / dot);

        add_v3_v3v3(out, l1, l_vec);

        return 1;
    }
}

/* note: return normal isnt unit length */
void isect_plane_plane_v3(float r_isect_co[3], float r_isect_no[3],
                          const float plane_a_co[3], const float plane_a_no[3],
                          const float plane_b_co[3], const float plane_b_no[3])
{
    float plane_a_co_other[3];
    cross_v3_v3v3(r_isect_no, plane_a_no, plane_b_no); /* direction is simply the cross product */
    cross_v3_v3v3(plane_a_co_other, plane_a_no, r_isect_no);
    add_v3_v3(plane_a_co_other, plane_a_co);
    isect_line_plane_v3(r_isect_co, plane_a_co, plane_a_co_other, plane_b_co, plane_b_no, FALSE);
}


/* Adapted from the paper by Kasper Fauerby */
/* "Improved Collision detection and Response" */
static int getLowestRoot(const float a, const float b, const float c, const float maxR, float *root)
{
    // Check if a solution exists
    float determinant = b*b - 4.0f*a*c;

    // If determinant is negative it means no solutions.
    if (determinant >= 0.0f)
    {
        // calculate the two roots: (if determinant == 0 then
        // x1==x2 but lets disregard that slight optimization)
        float sqrtD = (float)sqrt(determinant);
        float r1 = (-b - sqrtD) / (2.0f*a);
        float r2 = (-b + sqrtD) / (2.0f*a);
        
        // Sort so x1 <= x2
        if (r1 > r2)
            SWAP(float, r1, r2);

        // Get lowest root:
        if (r1 > 0.0f && r1 < maxR)
        {
            *root = r1;
            return 1;
        }

        // It is possible that we want x2 - this can happen
        // if x1 < 0
        if (r2 > 0.0f && r2 < maxR)
        {
            *root = r2;
            return 1;
        }
    }
    // No (valid) solutions
    return 0;
}

int isect_sweeping_sphere_tri_v3(
        const float p1[3], const float p2[3], const float radius,
        const float v0[3], const float v1[3], const float v2[3],
        float *r_lambda, float ipoint[3])
{
    float e1[3], e2[3], e3[3], point[3], vel[3], /*dist[3],*/ nor[3], temp[3], bv[3];
    float a, b, c, d, e, x, y, z, radius2=radius*radius;
    float elen2,edotv,edotbv,nordotv;
    float newLambda;
    int found_by_sweep=0;

    sub_v3_v3v3(e1,v1,v0);
    sub_v3_v3v3(e2,v2,v0);
    sub_v3_v3v3(vel,p2,p1);

/*---test plane of tri---*/
    cross_v3_v3v3(nor,e1,e2);
    normalize_v3(nor);

    /* flip normal */
    if(dot_v3v3(nor,vel)>0.0f) negate_v3(nor);
    
    a=dot_v3v3(p1,nor)-dot_v3v3(v0,nor);
    nordotv=dot_v3v3(nor,vel);

    if (fabsf(nordotv) < 0.000001f)
    {
        if(fabsf(a) >= radius) {
            return 0;
        }
    }
    else
    {
        float t0=(-a+radius)/nordotv;
        float t1=(-a-radius)/nordotv;

        if(t0>t1)
            SWAP(float, t0, t1);

        if(t0>1.0f || t1<0.0f) return 0;

        /* clamp to [0,1] */
        CLAMP(t0, 0.0f, 1.0f);
        CLAMP(t1, 0.0f, 1.0f);

        /*---test inside of tri---*/
        /* plane intersection point */

        point[0] = p1[0] + vel[0]*t0 - nor[0]*radius;
        point[1] = p1[1] + vel[1]*t0 - nor[1]*radius;
        point[2] = p1[2] + vel[2]*t0 - nor[2]*radius;


        /* is the point in the tri? */
        a=dot_v3v3(e1,e1);
        b=dot_v3v3(e1,e2);
        c=dot_v3v3(e2,e2);

        sub_v3_v3v3(temp,point,v0);
        d=dot_v3v3(temp,e1);
        e=dot_v3v3(temp,e2);
        
        x=d*c-e*b;
        y=e*a-d*b;
        z=x+y-(a*c-b*b);


        if(z <= 0.0f && (x >= 0.0f && y >= 0.0f))
        {
        //(((unsigned int)z)& ~(((unsigned int)x)|((unsigned int)y))) & 0x80000000){
            *r_lambda=t0;
            copy_v3_v3(ipoint,point);
            return 1;
        }
    }


    *r_lambda=1.0f;

/*---test points---*/
    a=dot_v3v3(vel,vel);

    /*v0*/
    sub_v3_v3v3(temp,p1,v0);
    b=2.0f*dot_v3v3(vel,temp);
    c=dot_v3v3(temp,temp)-radius2;

    if(getLowestRoot(a, b, c, *r_lambda, r_lambda))
    {
        copy_v3_v3(ipoint,v0);
        found_by_sweep=1;
    }

    /*v1*/
    sub_v3_v3v3(temp,p1,v1);
    b=2.0f*dot_v3v3(vel,temp);
    c=dot_v3v3(temp,temp)-radius2;

    if(getLowestRoot(a, b, c, *r_lambda, r_lambda))
    {
        copy_v3_v3(ipoint,v1);
        found_by_sweep=1;
    }
    
    /*v2*/
    sub_v3_v3v3(temp,p1,v2);
    b=2.0f*dot_v3v3(vel,temp);
    c=dot_v3v3(temp,temp)-radius2;

    if(getLowestRoot(a, b, c, *r_lambda, r_lambda))
    {
        copy_v3_v3(ipoint,v2);
        found_by_sweep=1;
    }

/*---test edges---*/
    sub_v3_v3v3(e3,v2,v1); //wasnt yet calculated


    /*e1*/
    sub_v3_v3v3(bv,v0,p1);

    elen2 = dot_v3v3(e1,e1);
    edotv = dot_v3v3(e1,vel);
    edotbv = dot_v3v3(e1,bv);

    a=elen2*(-dot_v3v3(vel,vel))+edotv*edotv;
    b=2.0f*(elen2*dot_v3v3(vel,bv)-edotv*edotbv);
    c=elen2*(radius2-dot_v3v3(bv,bv))+edotbv*edotbv;

    if(getLowestRoot(a, b, c, *r_lambda, &newLambda))
    {
        e=(edotv*newLambda-edotbv)/elen2;

        if(e >= 0.0f && e <= 1.0f)
        {
            *r_lambda = newLambda;
            copy_v3_v3(ipoint,e1);
            mul_v3_fl(ipoint,e);
            add_v3_v3(ipoint, v0);
            found_by_sweep=1;
        }
    }

    /*e2*/
    /*bv is same*/
    elen2 = dot_v3v3(e2,e2);
    edotv = dot_v3v3(e2,vel);
    edotbv = dot_v3v3(e2,bv);

    a=elen2*(-dot_v3v3(vel,vel))+edotv*edotv;
    b=2.0f*(elen2*dot_v3v3(vel,bv)-edotv*edotbv);
    c=elen2*(radius2-dot_v3v3(bv,bv))+edotbv*edotbv;

    if(getLowestRoot(a, b, c, *r_lambda, &newLambda))
    {
        e=(edotv*newLambda-edotbv)/elen2;

        if(e >= 0.0f && e <= 1.0f)
        {
            *r_lambda = newLambda;
            copy_v3_v3(ipoint,e2);
            mul_v3_fl(ipoint,e);
            add_v3_v3(ipoint, v0);
            found_by_sweep=1;
        }
    }

    /*e3*/
    /* sub_v3_v3v3(bv,v0,p1); */ /* UNUSED */
    /* elen2 = dot_v3v3(e1,e1); */ /* UNUSED */
    /* edotv = dot_v3v3(e1,vel); */ /* UNUSED */
    /* edotbv = dot_v3v3(e1,bv); */ /* UNUSED */

    sub_v3_v3v3(bv,v1,p1);
    elen2 = dot_v3v3(e3,e3);
    edotv = dot_v3v3(e3,vel);
    edotbv = dot_v3v3(e3,bv);

    a=elen2*(-dot_v3v3(vel,vel))+edotv*edotv;
    b=2.0f*(elen2*dot_v3v3(vel,bv)-edotv*edotbv);
    c=elen2*(radius2-dot_v3v3(bv,bv))+edotbv*edotbv;

    if(getLowestRoot(a, b, c, *r_lambda, &newLambda))
    {
        e=(edotv*newLambda-edotbv)/elen2;

        if(e >= 0.0f && e <= 1.0f)
        {
            *r_lambda = newLambda;
            copy_v3_v3(ipoint,e3);
            mul_v3_fl(ipoint,e);
            add_v3_v3(ipoint, v1);
            found_by_sweep=1;
        }
    }


    return found_by_sweep;
}
int isect_axial_line_tri_v3(const int axis, const float p1[3], const float p2[3],
                            const float v0[3], const float v1[3], const float v2[3], float *r_lambda)
{
    float p[3], e1[3], e2[3];
    float u, v, f;
    int a0=axis, a1=(axis+1)%3, a2=(axis+2)%3;

    //return isect_line_tri_v3(p1,p2,v0,v1,v2,lambda);

    //if(MIN3(v0[a1],v1[a1],v2[a1]) > p1[a1]) return 0;
    //if(MIN3(v0[a2],v1[a2],v2[a2]) > p1[a2]) return 0;
    //if(MAX3(v0[a1],v1[a1],v2[a1]) < p1[a1]) return 0;
    //if(MAX3(v0[a2],v1[a2],v2[a2]) < p1[a2]) return 0;

    
    sub_v3_v3v3(e1,v1,v0);
    sub_v3_v3v3(e2,v2,v0);
    sub_v3_v3v3(p,v0,p1);

    f= (e2[a1]*e1[a2]-e2[a2]*e1[a1]);
    if ((f > -0.000001f) && (f < 0.000001f)) return 0;

    v= (p[a2]*e1[a1]-p[a1]*e1[a2])/f;
    if ((v < 0.0f)||(v > 1.0f)) return 0;
    
    f= e1[a1];
    if((f > -0.000001f) && (f < 0.000001f)){
        f= e1[a2];
        if((f > -0.000001f) && (f < 0.000001f)) return 0;
        u= (-p[a2]-v*e2[a2])/f;
    }
    else
        u= (-p[a1]-v*e2[a1])/f;

    if ((u < 0.0f) || ((u + v) > 1.0f)) return 0;

    *r_lambda = (p[a0]+u*e1[a0]+v*e2[a0])/(p2[a0]-p1[a0]);

    if ((*r_lambda < 0.0f) || (*r_lambda > 1.0f)) return 0;

    return 1;
}

/* Returns the number of point of interests
 * 0 - lines are colinear
 * 1 - lines are coplanar, i1 is set to intersection
 * 2 - i1 and i2 are the nearest points on line 1 (v1, v2) and line 2 (v3, v4) respectively 
 * */
int isect_line_line_v3(const float v1[3], const float v2[3], const float v3[3], const float v4[3], float i1[3], float i2[3])
{
    float a[3], b[3], c[3], ab[3], cb[3], dir1[3], dir2[3];
    float d;
    
    sub_v3_v3v3(c, v3, v1);
    sub_v3_v3v3(a, v2, v1);
    sub_v3_v3v3(b, v4, v3);

    normalize_v3_v3(dir1, a);
    normalize_v3_v3(dir2, b);
    d = dot_v3v3(dir1, dir2);
    if (d == 1.0f || d == -1.0f) {
        /* colinear */
        return 0;
    }

    cross_v3_v3v3(ab, a, b);
    d = dot_v3v3(c, ab);

    /* test if the two lines are coplanar */
    if (d > -0.000001f && d < 0.000001f) {
        cross_v3_v3v3(cb, c, b);

        mul_v3_fl(a, dot_v3v3(cb, ab) / dot_v3v3(ab, ab));
        add_v3_v3v3(i1, v1, a);
        copy_v3_v3(i2, i1);
        
        return 1; /* one intersection only */
    }
    /* if not */
    else {
        float n[3], t[3];
        float v3t[3], v4t[3];
        sub_v3_v3v3(t, v1, v3);

        /* offset between both plane where the lines lies */
        cross_v3_v3v3(n, a, b);
        project_v3_v3v3(t, t, n);

        /* for the first line, offset the second line until it is coplanar */
        add_v3_v3v3(v3t, v3, t);
        add_v3_v3v3(v4t, v4, t);
        
        sub_v3_v3v3(c, v3t, v1);
        sub_v3_v3v3(a, v2, v1);
        sub_v3_v3v3(b, v4t, v3t);

        cross_v3_v3v3(ab, a, b);
        cross_v3_v3v3(cb, c, b);

        mul_v3_fl(a, dot_v3v3(cb, ab) / dot_v3v3(ab, ab));
        add_v3_v3v3(i1, v1, a);

        /* for the second line, just substract the offset from the first intersection point */
        sub_v3_v3v3(i2, i1, t);
        
        return 2; /* two nearest points */
    }
} 

/* Intersection point strictly between the two lines
 * 0 when no intersection is found 
 * */
int isect_line_line_strict_v3(const float v1[3], const float v2[3], const float v3[3], const float v4[3], float vi[3], float *r_lambda)
{
    float a[3], b[3], c[3], ab[3], cb[3], ca[3], dir1[3], dir2[3];
    float d;
    
    sub_v3_v3v3(c, v3, v1);
    sub_v3_v3v3(a, v2, v1);
    sub_v3_v3v3(b, v4, v3);

    normalize_v3_v3(dir1, a);
    normalize_v3_v3(dir2, b);
    d = dot_v3v3(dir1, dir2);
    if (d == 1.0f || d == -1.0f || d == 0) {
        /* colinear or one vector is zero-length*/
        return 0;
    }

    cross_v3_v3v3(ab, a, b);
    d = dot_v3v3(c, ab);

    /* test if the two lines are coplanar */
    if (d > -0.000001f && d < 0.000001f) {
        float f1, f2;
        cross_v3_v3v3(cb, c, b);
        cross_v3_v3v3(ca, c, a);

        f1 = dot_v3v3(cb, ab) / dot_v3v3(ab, ab);
        f2 = dot_v3v3(ca, ab) / dot_v3v3(ab, ab);
        
        if (f1 >= 0 && f1 <= 1 &&
            f2 >= 0 && f2 <= 1)
        {
            mul_v3_fl(a, f1);
            add_v3_v3v3(vi, v1, a);

            if (r_lambda) *r_lambda = f1;

            return 1; /* intersection found */
        }
        else
        {
            return 0;
        }
    }
    else
    {
        return 0;
    }
} 

int isect_aabb_aabb_v3(const float min1[3], const float max1[3], const float min2[3], const float max2[3])
{
    return (min1[0]<max2[0] && min1[1]<max2[1] && min1[2]<max2[2] &&
            min2[0]<max1[0] && min2[1]<max1[1] && min2[2]<max1[2]);
}

/* find closest point to p on line through l1,l2 and return lambda,
 * where (0 <= lambda <= 1) when cp is in the line segement l1,l2
 */
float closest_to_line_v3(float cp[3], const float p[3], const float l1[3], const float l2[3])
{
    float h[3],u[3],lambda;
    sub_v3_v3v3(u, l2, l1);
    sub_v3_v3v3(h, p, l1);
    lambda =dot_v3v3(u,h)/dot_v3v3(u,u);
    cp[0] = l1[0] + u[0] * lambda;
    cp[1] = l1[1] + u[1] * lambda;
    cp[2] = l1[2] + u[2] * lambda;
    return lambda;
}

float closest_to_line_v2(float cp[2],const float p[2], const float l1[2], const float l2[2])
{
    float h[2],u[2],lambda;
    sub_v2_v2v2(u, l2, l1);
    sub_v2_v2v2(h, p, l1);
    lambda =dot_v2v2(u,h)/dot_v2v2(u,u);
    cp[0] = l1[0] + u[0] * lambda;
    cp[1] = l1[1] + u[1] * lambda;
    return lambda;
}

/* little sister we only need to know lambda */
float line_point_factor_v3(const float p[3], const float l1[3], const float l2[3])
{
    float h[3],u[3];
    sub_v3_v3v3(u, l2, l1);
    sub_v3_v3v3(h, p, l1);
    return(dot_v3v3(u,h)/dot_v3v3(u,u));
}

float line_point_factor_v2(const float p[2], const float l1[2], const float l2[2])
{
    float h[2], u[2];
    sub_v2_v2v2(u, l2, l1);
    sub_v2_v2v2(h, p, l1);
    return(dot_v2v2(u, h)/dot_v2v2(u, u));
}

/* Similar to LineIntersectsTriangleUV, except it operates on a quad and in 2d, assumes point is in quad */
void isect_point_quad_uv_v2(const float v0[2], const float v1[2], const float v2[2], const float v3[2], const float pt[2], float r_uv[2])
{
    float x0,y0, x1,y1, wtot, v2d[2], w1, w2;
    
    /* used for parallel lines */
    float pt3d[3], l1[3], l2[3], pt_on_line[3];
    
    /* compute 2 edges  of the quad  intersection point */
    if (IsectLLPt2Df(v0[0],v0[1],v1[0],v1[1],  v2[0],v2[1],v3[0],v3[1], &x0,&y0) == 1) {
        /* the intersection point between the quad-edge intersection and the point in the quad we want the uv's for */
        /* should never be paralle !! */
        /*printf("\tnot parallel 1\n");*/
        IsectLLPt2Df(pt[0],pt[1],x0,y0,  v0[0],v0[1],v3[0],v3[1], &x1,&y1);
        
        /* Get the weights from the new intersection point, to each edge */
        v2d[0] = x1-v0[0];
        v2d[1] = y1-v0[1];
        w1 = len_v2(v2d);
        
        v2d[0] = x1-v3[0]; /* some but for the other vert */
        v2d[1] = y1-v3[1];
        w2 = len_v2(v2d);
        wtot = w1+w2;
        /*w1 = w1/wtot;*/
        /*w2 = w2/wtot;*/
        r_uv[0] = w1/wtot;
    } else {
        /* lines are parallel, lambda_cp_line_ex is 3d grrr */
        /*printf("\tparallel1\n");*/
        pt3d[0] = pt[0];
        pt3d[1] = pt[1];
        pt3d[2] = l1[2] = l2[2] = 0.0f;
        
        l1[0] = v0[0]; l1[1] = v0[1];
        l2[0] = v1[0]; l2[1] = v1[1];
        closest_to_line_v3(pt_on_line,pt3d, l1, l2);
        v2d[0] = pt[0]-pt_on_line[0]; /* same, for the other vert */
        v2d[1] = pt[1]-pt_on_line[1];
        w1 = len_v2(v2d);
        
        l1[0] = v2[0]; l1[1] = v2[1];
        l2[0] = v3[0]; l2[1] = v3[1];
        closest_to_line_v3(pt_on_line,pt3d, l1, l2);
        v2d[0] = pt[0]-pt_on_line[0]; /* same, for the other vert */
        v2d[1] = pt[1]-pt_on_line[1];
        w2 = len_v2(v2d);
        wtot = w1+w2;
        r_uv[0] = w1/wtot;
    }
    
    /* Same as above to calc the uv[1] value, alternate calculation */
    
    if (IsectLLPt2Df(v0[0],v0[1],v3[0],v3[1],  v1[0],v1[1],v2[0],v2[1], &x0,&y0) == 1) { /* was v0,v1  v2,v3  now v0,v3  v1,v2*/
        /* never paralle if above was not */
        /*printf("\tnot parallel2\n");*/
        IsectLLPt2Df(pt[0],pt[1],x0,y0,  v0[0],v0[1],v1[0],v1[1], &x1,&y1);/* was v0,v3  now v0,v1*/
        
        v2d[0] = x1-v0[0];
        v2d[1] = y1-v0[1];
        w1 = len_v2(v2d);
        
        v2d[0] = x1-v1[0];
        v2d[1] = y1-v1[1];
        w2 = len_v2(v2d);
        wtot = w1+w2;
        r_uv[1] = w1/wtot;
    } else {
        /* lines are parallel, lambda_cp_line_ex is 3d grrr */
        /*printf("\tparallel2\n");*/
        pt3d[0] = pt[0];
        pt3d[1] = pt[1];
        pt3d[2] = l1[2] = l2[2] = 0.0f;
        
        
        l1[0] = v0[0]; l1[1] = v0[1];
        l2[0] = v3[0]; l2[1] = v3[1];
        closest_to_line_v3(pt_on_line,pt3d, l1, l2);
        v2d[0] = pt[0]-pt_on_line[0]; /* some but for the other vert */
        v2d[1] = pt[1]-pt_on_line[1];
        w1 = len_v2(v2d);
        
        l1[0] = v1[0]; l1[1] = v1[1];
        l2[0] = v2[0]; l2[1] = v2[1];
        closest_to_line_v3(pt_on_line,pt3d, l1, l2);
        v2d[0] = pt[0]-pt_on_line[0]; /* some but for the other vert */
        v2d[1] = pt[1]-pt_on_line[1];
        w2 = len_v2(v2d);
        wtot = w1+w2;
        r_uv[1] = w1/wtot;
    }
    /* may need to flip UV's here */
}

/* same as above but does tri's and quads, tri's are a bit of a hack */
void isect_point_face_uv_v2(const int isquad, const float v0[2], const float v1[2], const float v2[2], const float v3[2], const float pt[2], float r_uv[2])
{
    if (isquad) {
        isect_point_quad_uv_v2(v0, v1, v2, v3, pt, r_uv);
    }
    else {
        /* not for quads, use for our abuse of LineIntersectsTriangleUV */
        float p1_3d[3], p2_3d[3], v0_3d[3], v1_3d[3], v2_3d[3], lambda;
            
        p1_3d[0] = p2_3d[0] = r_uv[0];
        p1_3d[1] = p2_3d[1] = r_uv[1];
        p1_3d[2] = 1.0f;
        p2_3d[2] = -1.0f;
        v0_3d[2] = v1_3d[2] = v2_3d[2] = 0.0;
        
        /* generate a new fuv, (this is possibly a non optimal solution,
         * since we only need 2d calculation but use 3d func's)
         * 
         * this method makes an imaginary triangle in 2d space using the UV's from the derived mesh face
         * Then find new uv coords using the fuv and this face with LineIntersectsTriangleUV.
         * This means the new values will be correct in relation to the derived meshes face. 
         */
        copy_v2_v2(v0_3d, v0);
        copy_v2_v2(v1_3d, v1);
        copy_v2_v2(v2_3d, v2);
        
        /* Doing this in 3D is not nice */
        isect_line_tri_v3(p1_3d, p2_3d, v0_3d, v1_3d, v2_3d, &lambda, r_uv);
    }
}

#if 0 // XXX this version used to be used in isect_point_tri_v2_int() and was called IsPointInTri2D
int isect_point_tri_v2(float pt[2], float v1[2], float v2[2], float v3[2])
{
    float inp1, inp2, inp3;
    
    inp1= (v2[0]-v1[0])*(v1[1]-pt[1]) + (v1[1]-v2[1])*(v1[0]-pt[0]);
    inp2= (v3[0]-v2[0])*(v2[1]-pt[1]) + (v2[1]-v3[1])*(v2[0]-pt[0]);
    inp3= (v1[0]-v3[0])*(v3[1]-pt[1]) + (v3[1]-v1[1])*(v3[0]-pt[0]);
    
    if(inp1<=0.0f && inp2<=0.0f && inp3<=0.0f) return 1;
    if(inp1>=0.0f && inp2>=0.0f && inp3>=0.0f) return 1;
    
    return 0;
}
#endif

#if 0
int isect_point_tri_v2(float v0[2], float v1[2], float v2[2], float pt[2])
{
        /* not for quads, use for our abuse of LineIntersectsTriangleUV */
        float p1_3d[3], p2_3d[3], v0_3d[3], v1_3d[3], v2_3d[3];
        /* not used */
        float lambda, uv[3];
            
        p1_3d[0] = p2_3d[0] = uv[0]= pt[0];
        p1_3d[1] = p2_3d[1] = uv[1]= uv[2]= pt[1];
        p1_3d[2] = 1.0f;
        p2_3d[2] = -1.0f;
        v0_3d[2] = v1_3d[2] = v2_3d[2] = 0.0;
        
        /* generate a new fuv, (this is possibly a non optimal solution,
         * since we only need 2d calculation but use 3d func's)
         * 
         * this method makes an imaginary triangle in 2d space using the UV's from the derived mesh face
         * Then find new uv coords using the fuv and this face with LineIntersectsTriangleUV.
         * This means the new values will be correct in relation to the derived meshes face. 
         */
        copy_v2_v2(v0_3d, v0);
        copy_v2_v2(v1_3d, v1);
        copy_v2_v2(v2_3d, v2);
        
        /* Doing this in 3D is not nice */
        return isect_line_tri_v3(p1_3d, p2_3d, v0_3d, v1_3d, v2_3d, &lambda, uv);
}
#endif

/*

    x1,y2
    |  \
    |   \     .(a,b)
    |    \
    x1,y1-- x2,y1

*/
int isect_point_tri_v2_int(const int x1, const int y1, const int x2, const int y2, const int a, const int b)
{
    float v1[2], v2[2], v3[2], p[2];
    
    v1[0]= (float)x1;
    v1[1]= (float)y1;
    
    v2[0]= (float)x1;
    v2[1]= (float)y2;
    
    v3[0]= (float)x2;
    v3[1]= (float)y1;
    
    p[0]= (float)a;
    p[1]= (float)b;
    
    return isect_point_tri_v2(p, v1, v2, v3);
}

static int point_in_slice(const float p[3], const float v1[3], const float l1[3], const float l2[3])
{
/* 
what is a slice ?
some maths:
a line including l1,l2 and a point not on the line 
define a subset of R3 delimeted by planes parallel to the line and orthogonal 
to the (point --> line) distance vector,one plane on the line one on the point, 
the room inside usually is rather small compared to R3 though still infinte
useful for restricting (speeding up) searches 
e.g. all points of triangular prism are within the intersection of 3 'slices'
onother trivial case : cube 
but see a 'spat' which is a deformed cube with paired parallel planes needs only 3 slices too
*/
    float h,rp[3],cp[3],q[3];

    closest_to_line_v3(cp,v1,l1,l2);
    sub_v3_v3v3(q,cp,v1);

    sub_v3_v3v3(rp,p,v1);
    h=dot_v3v3(q,rp)/dot_v3v3(q,q);
    if (h < 0.0f || h > 1.0f) return 0;
    return 1;
}

#if 0
/*adult sister defining the slice planes by the origin and the normal  
NOTE |normal| may not be 1 but defining the thickness of the slice*/
static int point_in_slice_as(float p[3],float origin[3],float normal[3])
{
    float h,rp[3];
    sub_v3_v3v3(rp,p,origin);
    h=dot_v3v3(normal,rp)/dot_v3v3(normal,normal);
    if (h < 0.0f || h > 1.0f) return 0;
    return 1;
}

/*mama (knowing the squared length of the normal)*/
static int point_in_slice_m(float p[3],float origin[3],float normal[3],float lns)
{
    float h,rp[3];
    sub_v3_v3v3(rp,p,origin);
    h=dot_v3v3(normal,rp)/lns;
    if (h < 0.0f || h > 1.0f) return 0;
    return 1;
}
#endif

int isect_point_tri_prism_v3(const float p[3], const float v1[3], const float v2[3], const float v3[3])
{
    if(!point_in_slice(p,v1,v2,v3)) return 0;
    if(!point_in_slice(p,v2,v3,v1)) return 0;
    if(!point_in_slice(p,v3,v1,v2)) return 0;
    return 1;
}

int clip_line_plane(float p1[3], float p2[3], const float plane[4])
{
    float dp[3], n[3], div, t, pc[3];

    copy_v3_v3(n, plane);
    sub_v3_v3v3(dp, p2, p1);
    div= dot_v3v3(dp, n);

    if(div == 0.0f) /* parallel */
        return 1;

    t= -(dot_v3v3(p1, n) + plane[3])/div;

    if(div > 0.0f) {
        /* behind plane, completely clipped */
        if(t >= 1.0f) {
            zero_v3(p1);
            zero_v3(p2);
            return 0;
        }

        /* intersect plane */
        if(t > 0.0f) {
            madd_v3_v3v3fl(pc, p1, dp, t);
            copy_v3_v3(p1, pc);
            return 1;
        }

        return 1;
    }
    else {
        /* behind plane, completely clipped */
        if(t <= 0.0f) {
            zero_v3(p1);
            zero_v3(p2);
            return 0;
        }

        /* intersect plane */
        if(t < 1.0f) {
            madd_v3_v3v3fl(pc, p1, dp, t);
            copy_v3_v3(p2, pc);
            return 1;
        }

        return 1;
    }
}


void plot_line_v2v2i(const int p1[2], const int p2[2], int (*callback)(int, int, void *), void *userData)
{
    int x1= p1[0];
    int y1= p1[1];
    int x2= p2[0];
    int y2= p2[1];

    signed char ix;
    signed char iy;

    // if x1 == x2 or y1 == y2, then it does not matter what we set here
    int delta_x = (x2 > x1?(ix = 1, x2 - x1):(ix = -1, x1 - x2)) << 1;
    int delta_y = (y2 > y1?(iy = 1, y2 - y1):(iy = -1, y1 - y2)) << 1;

    if(callback(x1, y1, userData) == 0) {
        return;
    }

    if (delta_x >= delta_y) {
        // error may go below zero
        int error = delta_y - (delta_x >> 1);

        while (x1 != x2) {
            if (error >= 0) {
                if (error || (ix > 0)) {
                    y1 += iy;
                    error -= delta_x;
                }
                // else do nothing
            }
            // else do nothing

            x1 += ix;
            error += delta_y;

            if(callback(x1, y1, userData) == 0) {
                return ;
            }
        }
    }
    else {
        // error may go below zero
        int error = delta_x - (delta_y >> 1);

        while (y1 != y2) {
            if (error >= 0) {
                if (error || (iy > 0)) {
                    x1 += ix;
                    error -= delta_y;
                }
                // else do nothing
            }
            // else do nothing

            y1 += iy;
            error += delta_x;

            if(callback(x1, y1, userData) == 0) {
                return;
            }
        }
    }
}

/****************************** Interpolation ********************************/

/* get the 2 dominant axis values, 0==X, 1==Y, 2==Z */
void axis_dominant_v3(int *axis_a, int *axis_b, const float axis[3])
{
    const float xn= fabsf(axis[0]);
    const float yn= fabsf(axis[1]);
    const float zn= fabsf(axis[2]);

    if      (zn >= xn && zn >= yn) { *axis_a= 0; *axis_b= 1; }
    else if (yn >= xn && yn >= zn) { *axis_a= 0; *axis_b= 2; }
    else                           { *axis_a= 1; *axis_b= 2; }
}

static float tri_signed_area(const float v1[3], const float v2[3], const float v3[3], const int i, const int j)
{
    return 0.5f*((v1[i]-v2[i])*(v2[j]-v3[j]) + (v1[j]-v2[j])*(v3[i]-v2[i]));
}

static int barycentric_weights(const float v1[3], const float v2[3], const float v3[3], const float co[3], const float n[3], float w[3])
{
    float a1, a2, a3, asum;
    int i, j;

    axis_dominant_v3(&i, &j, n);

    a1= tri_signed_area(v2, v3, co, i, j);
    a2= tri_signed_area(v3, v1, co, i, j);
    a3= tri_signed_area(v1, v2, co, i, j);

    asum= a1 + a2 + a3;

    if (fabsf(asum) < FLT_EPSILON) {
        /* zero area triangle */
        w[0]= w[1]= w[2]= 1.0f/3.0f;
        return 1;
    }

    asum= 1.0f/asum;
    w[0]= a1*asum;
    w[1]= a2*asum;
    w[2]= a3*asum;

    return 0;
}

void interp_weights_face_v3(float w[4], const float v1[3], const float v2[3], const float v3[3], const float v4[3], const float co[3])
{
    float w2[3];

    w[0]= w[1]= w[2]= w[3]= 0.0f;

    /* first check for exact match */
    if(equals_v3v3(co, v1))
        w[0]= 1.0f;
    else if(equals_v3v3(co, v2))
        w[1]= 1.0f;
    else if(equals_v3v3(co, v3))
        w[2]= 1.0f;
    else if(v4 && equals_v3v3(co, v4))
        w[3]= 1.0f;
    else {
        /* otherwise compute barycentric interpolation weights */
        float n1[3], n2[3], n[3];
        int degenerate;

        sub_v3_v3v3(n1, v1, v3);
        if (v4) {
            sub_v3_v3v3(n2, v2, v4);
        }
        else {
            sub_v3_v3v3(n2, v2, v3);
        }
        cross_v3_v3v3(n, n1, n2);

        /* OpenGL seems to split this way, so we do too */
        if (v4) {
            degenerate= barycentric_weights(v1, v2, v4, co, n, w);
            SWAP(float, w[2], w[3]);

            if(degenerate || (w[0] < 0.0f)) {
                /* if w[1] is negative, co is on the other side of the v1-v3 edge,
                   so we interpolate using the other triangle */
                degenerate= barycentric_weights(v2, v3, v4, co, n, w2);

                if(!degenerate) {
                    w[0]= 0.0f;
                    w[1]= w2[0];
                    w[2]= w2[1];
                    w[3]= w2[2];
                }
            }
        }
        else
            barycentric_weights(v1, v2, v3, co, n, w);
    }
}

/* used by projection painting
 * note: using area_tri_signed_v2 means locations outside the triangle are correctly weighted */
void barycentric_weights_v2(const float v1[2], const float v2[2], const float v3[2], const float co[2], float w[3])
{
    float wtot_inv, wtot;

    w[0] = area_tri_signed_v2(v2, v3, co);
    w[1] = area_tri_signed_v2(v3, v1, co);
    w[2] = area_tri_signed_v2(v1, v2, co);
    wtot = w[0]+w[1]+w[2];

    if (wtot != 0.0f) {
        wtot_inv = 1.0f/wtot;

        w[0] = w[0]*wtot_inv;
        w[1] = w[1]*wtot_inv;
        w[2] = w[2]*wtot_inv;
    }
    else /* dummy values for zero area face */
        w[0] = w[1] = w[2] = 1.0f/3.0f;
}

/* given 2 triangles in 3D space, and a point in relation to the first triangle.
 * calculate the location of a point in relation to the second triangle.
 * Useful for finding relative positions with geometry */
void barycentric_transform(float pt_tar[3], float const pt_src[3],
        const float tri_tar_p1[3], const float tri_tar_p2[3], const float tri_tar_p3[3],
        const float tri_src_p1[3], const float tri_src_p2[3], const float tri_src_p3[3])
{
    /* this works by moving the source triangle so its normal is pointing on the Z
     * axis where its barycentric wights can be calculated in 2D and its Z offset can
     *  be re-applied. The weights are applied directly to the targets 3D points and the
     *  z-depth is used to scale the targets normal as an offset.
     * This saves transforming the target into its Z-Up orientation and back (which could also work) */
    const float z_up[3] = {0, 0, 1};
    float no_tar[3], no_src[3];
    float quat_src[4];
    float pt_src_xy[3];
    float  tri_xy_src[3][3];
    float w_src[3];
    float area_tar, area_src;
    float z_ofs_src;

    normal_tri_v3(no_tar, tri_tar_p1, tri_tar_p2, tri_tar_p3);
    normal_tri_v3(no_src, tri_src_p1, tri_src_p2, tri_src_p3);

    rotation_between_vecs_to_quat(quat_src, no_src, z_up);
    normalize_qt(quat_src);

    copy_v3_v3(pt_src_xy, pt_src);
    copy_v3_v3(tri_xy_src[0], tri_src_p1);
    copy_v3_v3(tri_xy_src[1], tri_src_p2);
    copy_v3_v3(tri_xy_src[2], tri_src_p3);

    /* make the source tri xy space */
    mul_qt_v3(quat_src, pt_src_xy);
    mul_qt_v3(quat_src, tri_xy_src[0]);
    mul_qt_v3(quat_src, tri_xy_src[1]);
    mul_qt_v3(quat_src, tri_xy_src[2]);

    barycentric_weights_v2(tri_xy_src[0], tri_xy_src[1], tri_xy_src[2], pt_src_xy, w_src);
    interp_v3_v3v3v3(pt_tar, tri_tar_p1, tri_tar_p2, tri_tar_p3, w_src);

    area_tar= sqrtf(area_tri_v3(tri_tar_p1, tri_tar_p2, tri_tar_p3));
    area_src= sqrtf(area_tri_v2(tri_xy_src[0], tri_xy_src[1], tri_xy_src[2]));

    z_ofs_src= pt_src_xy[2] - tri_xy_src[0][2];
    madd_v3_v3v3fl(pt_tar, pt_tar, no_tar, (z_ofs_src / area_src) * area_tar);
}

/* given an array with some invalid values this function interpolates valid values
 * replacing the invalid ones */
int interp_sparse_array(float *array, int const list_size, const float skipval)
{
    int found_invalid = 0;
    int found_valid = 0;
    int i;

    for (i=0; i < list_size; i++) {
        if(array[i] == skipval)
            found_invalid= 1;
        else
            found_valid= 1;
    }

    if(found_valid==0) {
        return -1;
    }
    else if (found_invalid==0) {
        return 0;
    }
    else {
        /* found invalid depths, interpolate */
        float valid_last= skipval;
        int valid_ofs= 0;

        float *array_up= MEM_callocN(sizeof(float) * list_size, "interp_sparse_array up");
        float *array_down= MEM_callocN(sizeof(float) * list_size, "interp_sparse_array up");

        int *ofs_tot_up= MEM_callocN(sizeof(int) * list_size, "interp_sparse_array tup");
        int *ofs_tot_down= MEM_callocN(sizeof(int) * list_size, "interp_sparse_array tdown");

        for (i=0; i < list_size; i++) {
            if(array[i] == skipval) {
                array_up[i]= valid_last;
                ofs_tot_up[i]= ++valid_ofs;
            }
            else {
                valid_last= array[i];
                valid_ofs= 0;
            }
        }

        valid_last= skipval;
        valid_ofs= 0;

        for (i=list_size-1; i >= 0; i--) {
            if(array[i] == skipval) {
                array_down[i]= valid_last;
                ofs_tot_down[i]= ++valid_ofs;
            }
            else {
                valid_last= array[i];
                valid_ofs= 0;
            }
        }

        /* now blend */
        for (i=0; i < list_size; i++) {
            if(array[i] == skipval) {
                if(array_up[i] != skipval && array_down[i] != skipval) {
                    array[i]= ((array_up[i] * ofs_tot_down[i]) +  (array_down[i] * ofs_tot_up[i])) / (float)(ofs_tot_down[i] + ofs_tot_up[i]);
                } else if (array_up[i] != skipval) {
                    array[i]= array_up[i];
                } else if (array_down[i] != skipval) {
                    array[i]= array_down[i];
                }
            }
        }

        MEM_freeN(array_up);
        MEM_freeN(array_down);

        MEM_freeN(ofs_tot_up);
        MEM_freeN(ofs_tot_down);
    }

    return 1;
}

/* Mean value weights - smooth interpolation weights for polygons with
 * more than 3 vertices */
static float mean_value_half_tan(const float v1[3], const float v2[3], const float v3[3])
{
    float d2[3], d3[3], cross[3], area, dot, len;

    sub_v3_v3v3(d2, v2, v1);
    sub_v3_v3v3(d3, v3, v1);
    cross_v3_v3v3(cross, d2, d3);

    area= len_v3(cross);
    dot= dot_v3v3(d2, d3);
    len= len_v3(d2)*len_v3(d3);

    if(area == 0.0f)
        return 0.0f;
    else
        return (len - dot)/area;
}

void interp_weights_poly_v3(float *w, float v[][3], const int n, const float co[3])
{
    float totweight, t1, t2, len, *vmid, *vprev, *vnext;
    int i;

    totweight= 0.0f;

    for(i=0; i<n; i++) {
        vmid= v[i];
        vprev= (i == 0)? v[n-1]: v[i-1];
        vnext= (i == n-1)? v[0]: v[i+1];

        t1= mean_value_half_tan(co, vprev, vmid);
        t2= mean_value_half_tan(co, vmid, vnext);

        len= len_v3v3(co, vmid);
        w[i]= (t1+t2)/len;
        totweight += w[i];
    }

    if(totweight != 0.0f)
        for(i=0; i<n; i++)
            w[i] /= totweight;
}

/* (x1,v1)(t1=0)------(x2,v2)(t2=1), 0<t<1 --> (x,v)(t) */
void interp_cubic_v3(float x[3], float v[3], const float x1[3], const float v1[3], const float x2[3], const float v2[3], const float t)
{
    float a[3],b[3];
    float t2= t*t;
    float t3= t2*t;

    /* cubic interpolation */
    a[0]= v1[0] + v2[0] + 2*(x1[0] - x2[0]);
    a[1]= v1[1] + v2[1] + 2*(x1[1] - x2[1]);
    a[2]= v1[2] + v2[2] + 2*(x1[2] - x2[2]);

    b[0]= -2*v1[0] - v2[0] - 3*(x1[0] - x2[0]);
    b[1]= -2*v1[1] - v2[1] - 3*(x1[1] - x2[1]);
    b[2]= -2*v1[2] - v2[2] - 3*(x1[2] - x2[2]);

    x[0]= a[0]*t3 + b[0]*t2 + v1[0]*t + x1[0];
    x[1]= a[1]*t3 + b[1]*t2 + v1[1]*t + x1[1];
    x[2]= a[2]*t3 + b[2]*t2 + v1[2]*t + x1[2];

    v[0]= 3*a[0]*t2 + 2*b[0]*t + v1[0];
    v[1]= 3*a[1]*t2 + 2*b[1]*t + v1[1];
    v[2]= 3*a[2]*t2 + 2*b[2]*t + v1[2];
}

/* unfortunately internal calculations have to be done at double precision to achieve correct/stable results. */

#define IS_ZERO(x) ((x>(-DBL_EPSILON) && x<DBL_EPSILON) ? 1 : 0)

/* Barycentric reverse  */
void resolve_tri_uv(float r_uv[2], const float st[2], const float st0[2], const float st1[2], const float st2[2])
{
    /* find UV such that
       t= u*t0 + v*t1 + (1-u-v)*t2
       u*(t0-t2) + v*(t1-t2)= t-t2 */
    const double a= st0[0]-st2[0], b= st1[0]-st2[0];
    const double c= st0[1]-st2[1], d= st1[1]-st2[1];
    const double det= a*d - c*b;

    if(IS_ZERO(det)==0) {  /* det should never be zero since the determinant is the signed ST area of the triangle. */
        const double x[]= {st[0]-st2[0], st[1]-st2[1]};

        r_uv[0]= (float)((d*x[0] - b*x[1])/det);
        r_uv[1]= (float)(((-c)*x[0] + a*x[1])/det);
    } else zero_v2(r_uv);
}

/* bilinear reverse */
void resolve_quad_uv(float r_uv[2], const float st[2], const float st0[2], const float st1[2], const float st2[2], const float st3[2])
{
    const double signed_area= (st0[0]*st1[1] - st0[1]*st1[0]) + (st1[0]*st2[1] - st1[1]*st2[0]) +
                              (st2[0]*st3[1] - st2[1]*st3[0]) + (st3[0]*st0[1] - st3[1]*st0[0]);

    /* X is 2D cross product (determinant)
       A= (p0-p) X (p0-p3)*/
    const double a= (st0[0]-st[0])*(st0[1]-st3[1]) - (st0[1]-st[1])*(st0[0]-st3[0]);

    /* B= ( (p0-p) X (p1-p2) + (p1-p) X (p0-p3) ) / 2 */
    const double b= 0.5 * ( ((st0[0]-st[0])*(st1[1]-st2[1]) - (st0[1]-st[1])*(st1[0]-st2[0])) +
                             ((st1[0]-st[0])*(st0[1]-st3[1]) - (st1[1]-st[1])*(st0[0]-st3[0])) );

    /* C = (p1-p) X (p1-p2) */
    const double fC= (st1[0]-st[0])*(st1[1]-st2[1]) - (st1[1]-st[1])*(st1[0]-st2[0]);
    const double denom= a - 2*b + fC;

    // clear outputs
    zero_v2(r_uv);

    if(IS_ZERO(denom)!=0) {
        const double fDen= a-fC;
        if(IS_ZERO(fDen)==0)
            r_uv[0]= (float)(a / fDen);
    } else {
        const double desc_sq= b*b - a*fC;
        const double desc= sqrt(desc_sq<0.0?0.0:desc_sq);
        const double s= signed_area>0 ? (-1.0) : 1.0;

        r_uv[0]= (float)(( (a-b) + s * desc ) / denom);
    }

    /* find UV such that
      fST = (1-u)(1-v)*ST0 + u*(1-v)*ST1 + u*v*ST2 + (1-u)*v*ST3 */
    {
        const double denom_s= (1-r_uv[0])*(st0[0]-st3[0]) + r_uv[0]*(st1[0]-st2[0]);
        const double denom_t= (1-r_uv[0])*(st0[1]-st3[1]) + r_uv[0]*(st1[1]-st2[1]);
        int i= 0; double denom= denom_s;

        if(fabs(denom_s)<fabs(denom_t)) {
            i= 1;
            denom=denom_t;
        }

        if(IS_ZERO(denom)==0)
            r_uv[1]= (float) (( (1.0f-r_uv[0])*(st0[i]-st[i]) + r_uv[0]*(st1[i]-st[i]) ) / denom);
    }
}

#undef IS_ZERO

/***************************** View & Projection *****************************/

void orthographic_m4(float matrix[][4], const float left, const float right, const float bottom, const float top, const float nearClip, const float farClip)
{
    float Xdelta, Ydelta, Zdelta;
 
    Xdelta = right - left;
    Ydelta = top - bottom;
    Zdelta = farClip - nearClip;
    if (Xdelta == 0.0f || Ydelta == 0.0f || Zdelta == 0.0f) {
        return;
    }
    unit_m4(matrix);
    matrix[0][0] = 2.0f/Xdelta;
    matrix[3][0] = -(right + left)/Xdelta;
    matrix[1][1] = 2.0f/Ydelta;
    matrix[3][1] = -(top + bottom)/Ydelta;
    matrix[2][2] = -2.0f/Zdelta;        /* note: negate Z   */
    matrix[3][2] = -(farClip + nearClip)/Zdelta;
}

void perspective_m4(float mat[4][4], const float left, const float right, const float bottom, const float top, const float nearClip, const float farClip)
{
    float Xdelta, Ydelta, Zdelta;

    Xdelta = right - left;
    Ydelta = top - bottom;
    Zdelta = farClip - nearClip;

    if (Xdelta == 0.0f || Ydelta == 0.0f || Zdelta == 0.0f) {
        return;
    }
    mat[0][0] = nearClip * 2.0f/Xdelta;
    mat[1][1] = nearClip * 2.0f/Ydelta;
    mat[2][0] = (right + left)/Xdelta;      /* note: negate Z   */
    mat[2][1] = (top + bottom)/Ydelta;
    mat[2][2] = -(farClip + nearClip)/Zdelta;
    mat[2][3] = -1.0f;
    mat[3][2] = (-2.0f * nearClip * farClip)/Zdelta;
    mat[0][1] = mat[0][2] = mat[0][3] =
        mat[1][0] = mat[1][2] = mat[1][3] =
        mat[3][0] = mat[3][1] = mat[3][3] = 0.0;

}

/* translate a matrix created by orthographic_m4 or perspective_m4 in XY coords (used to jitter the view) */
void window_translate_m4(float winmat[][4], float perspmat[][4], const float x, const float y)
{
    if(winmat[2][3] == -1.0f) {
        /* in the case of a win-matrix, this means perspective always */
        float v1[3];
        float v2[3];
        float len1, len2;

        v1[0]= perspmat[0][0];
        v1[1]= perspmat[1][0];
        v1[2]= perspmat[2][0];

        v2[0]= perspmat[0][1];
        v2[1]= perspmat[1][1];
        v2[2]= perspmat[2][1];

        len1= (1.0f / len_v3(v1));
        len2= (1.0f / len_v3(v2));

        winmat[2][0] += len1 * winmat[0][0] * x;
        winmat[2][1] += len2 * winmat[1][1] * y;
    }
    else {
        winmat[3][0] += x;
        winmat[3][1] += y;
    }
}

static void i_multmatrix(float icand[][4], float Vm[][4])
{
    int row, col;
    float temp[4][4];

    for(row=0 ; row<4 ; row++) 
        for(col=0 ; col<4 ; col++)
            temp[row][col] = icand[row][0] * Vm[0][col]
                           + icand[row][1] * Vm[1][col]
                           + icand[row][2] * Vm[2][col]
                           + icand[row][3] * Vm[3][col];
    copy_m4_m4(Vm, temp);
}


void polarview_m4(float Vm[][4],float dist, float azimuth, float incidence, float twist)
{

    unit_m4(Vm);

    translate_m4(Vm,0.0, 0.0, -dist);
    rotate_m4(Vm,'Z',-twist);
    rotate_m4(Vm,'X',-incidence);
    rotate_m4(Vm,'Z',-azimuth);
}

void lookat_m4(float mat[][4],float vx, float vy, float vz, float px, float py, float pz, float twist)
{
    float sine, cosine, hyp, hyp1, dx, dy, dz;
    float mat1[4][4]= MAT4_UNITY;
    
    unit_m4(mat);

    rotate_m4(mat, 'Z', -twist);

    dx = px - vx;
    dy = py - vy;
    dz = pz - vz;
    hyp = dx * dx + dz * dz;    /* hyp squared  */
    hyp1 = (float)sqrt(dy*dy + hyp);
    hyp = (float)sqrt(hyp);     /* the real hyp */
    
    if (hyp1 != 0.0f) {     /* rotate X */
        sine = -dy / hyp1;
        cosine = hyp /hyp1;
    } else {
        sine = 0;
        cosine = 1.0f;
    }
    mat1[1][1] = cosine;
    mat1[1][2] = sine;
    mat1[2][1] = -sine;
    mat1[2][2] = cosine;
    
    i_multmatrix(mat1, mat);

    mat1[1][1] = mat1[2][2] = 1.0f; /* be careful here to reinit    */
    mat1[1][2] = mat1[2][1] = 0.0;  /* those modified by the last   */
    
    /* paragraph    */
    if (hyp != 0.0f) {          /* rotate Y */
        sine = dx / hyp;
        cosine = -dz / hyp;
    } else {
        sine = 0;
        cosine = 1.0f;
    }
    mat1[0][0] = cosine;
    mat1[0][2] = -sine;
    mat1[2][0] = sine;
    mat1[2][2] = cosine;
    
    i_multmatrix(mat1, mat);
    translate_m4(mat,-vx,-vy,-vz);  /* translate viewpoint to origin */
}

int box_clip_bounds_m4(float boundbox[2][3], const float bounds[4], float winmat[4][4])
{
    float mat[4][4], vec[4];
    int a, fl, flag= -1;

    copy_m4_m4(mat, winmat);

    for(a=0; a<8; a++) {
        vec[0]= (a & 1)? boundbox[0][0]: boundbox[1][0];
        vec[1]= (a & 2)? boundbox[0][1]: boundbox[1][1];
        vec[2]= (a & 4)? boundbox[0][2]: boundbox[1][2];
        vec[3]= 1.0;
        mul_m4_v4(mat, vec);

        fl= 0;
        if(bounds) {
            if(vec[0] > bounds[1]*vec[3]) fl |= 1;
            if(vec[0]< bounds[0]*vec[3]) fl |= 2;
            if(vec[1] > bounds[3]*vec[3]) fl |= 4;
            if(vec[1]< bounds[2]*vec[3]) fl |= 8;
        }
        else {
            if(vec[0] < -vec[3]) fl |= 1;
            if(vec[0] > vec[3]) fl |= 2;
            if(vec[1] < -vec[3]) fl |= 4;
            if(vec[1] > vec[3]) fl |= 8;
        }
        if(vec[2] < -vec[3]) fl |= 16;
        if(vec[2] > vec[3]) fl |= 32;

        flag &= fl;
        if(flag==0) return 0;
    }

    return flag;
}

void box_minmax_bounds_m4(float min[3], float max[3], float boundbox[2][3], float mat[4][4])
{
    float mn[3], mx[3], vec[3];
    int a;

    copy_v3_v3(mn, min);
    copy_v3_v3(mx, max);

    for(a=0; a<8; a++) {
        vec[0]= (a & 1)? boundbox[0][0]: boundbox[1][0];
        vec[1]= (a & 2)? boundbox[0][1]: boundbox[1][1];
        vec[2]= (a & 4)? boundbox[0][2]: boundbox[1][2];

        mul_m4_v3(mat, vec);
        DO_MINMAX(vec, mn, mx);
    }

    copy_v3_v3(min, mn);
    copy_v3_v3(max, mx);
}

/********************************** Mapping **********************************/

void map_to_tube(float *u, float *v, const float x, const float y, const float z)
{
    float len;
    
    *v = (z + 1.0f) / 2.0f;
    
    len= (float)sqrt(x*x+y*y);
    if(len > 0.0f)
        *u = (float)((1.0 - (atan2(x/len,y/len) / M_PI)) / 2.0);
    else
        *v = *u = 0.0f; /* to avoid un-initialized variables */
}

void map_to_sphere(float *u, float *v, const float x, const float y, const float z)
{
    float len;
    
    len= (float)sqrt(x*x+y*y+z*z);
    if(len > 0.0f) {
        if(x==0.0f && y==0.0f) *u= 0.0f;    /* othwise domain error */
        else *u = (1.0f - atan2f(x,y) / (float)M_PI) / 2.0f;

        *v = 1.0f - (float)saacos(z/len)/(float)M_PI;
    } else {
        *v = *u = 0.0f; /* to avoid un-initialized variables */
    }
}

/********************************* Normals **********************************/

void accumulate_vertex_normals(float n1[3], float n2[3], float n3[3],
    float n4[3], const float f_no[3], const float co1[3], const float co2[3],
    const float co3[3], const float co4[3])
{
    float vdiffs[4][3];
    const int nverts= (n4!=NULL && co4!=NULL)? 4: 3;

    /* compute normalized edge vectors */
    sub_v3_v3v3(vdiffs[0], co2, co1);
    sub_v3_v3v3(vdiffs[1], co3, co2);

    if(nverts==3) {
        sub_v3_v3v3(vdiffs[2], co1, co3);
    }
    else {
        sub_v3_v3v3(vdiffs[2], co4, co3);
        sub_v3_v3v3(vdiffs[3], co1, co4);
        normalize_v3(vdiffs[3]);
    }

    normalize_v3(vdiffs[0]);
    normalize_v3(vdiffs[1]);
    normalize_v3(vdiffs[2]);

    /* accumulate angle weighted face normal */
    {
        float *vn[]= {n1, n2, n3, n4};
        const float *prev_edge = vdiffs[nverts-1];
        int i;

        for(i=0; i<nverts; i++) {
            const float *cur_edge= vdiffs[i];
            const float fac= saacos(-dot_v3v3(cur_edge, prev_edge));

            // accumulate
            madd_v3_v3fl(vn[i], f_no, fac);
            prev_edge = cur_edge;
        }
    }
}

/********************************* Tangents **********************************/

/* For normal map tangents we need to detect uv boundaries, and only average
 * tangents in case the uvs are connected. Alternative would be to store 1 
 * tangent per face rather than 4 per face vertex, but that's not compatible
 * with games */


/* from BKE_mesh.h */
#define STD_UV_CONNECT_LIMIT    0.0001f

void sum_or_add_vertex_tangent(void *arena, VertexTangent **vtang, const float tang[3], const float uv[2])
{
    VertexTangent *vt;

    /* find a tangent with connected uvs */
    for(vt= *vtang; vt; vt=vt->next) {
        if(fabsf(uv[0]-vt->uv[0]) < STD_UV_CONNECT_LIMIT && fabsf(uv[1]-vt->uv[1]) < STD_UV_CONNECT_LIMIT) {
            add_v3_v3(vt->tang, tang);
            return;
        }
    }

    /* if not found, append a new one */
    vt= BLI_memarena_alloc((MemArena *)arena, sizeof(VertexTangent));
    copy_v3_v3(vt->tang, tang);
    vt->uv[0]= uv[0];
    vt->uv[1]= uv[1];

    if(*vtang)
        vt->next= *vtang;
    *vtang= vt;
}

float *find_vertex_tangent(VertexTangent *vtang, const float uv[2])
{
    VertexTangent *vt;
    static float nulltang[3] = {0.0f, 0.0f, 0.0f};

    for(vt= vtang; vt; vt=vt->next)
        if(fabsf(uv[0]-vt->uv[0]) < STD_UV_CONNECT_LIMIT && fabsf(uv[1]-vt->uv[1]) < STD_UV_CONNECT_LIMIT)
            return vt->tang;

    return nulltang;    /* shouldn't happen, except for nan or so */
}

void tangent_from_uv(float uv1[2], float uv2[2], float uv3[3], float co1[3], float co2[3], float co3[3], float n[3], float tang[3])
{
    float s1= uv2[0] - uv1[0];
    float s2= uv3[0] - uv1[0];
    float t1= uv2[1] - uv1[1];
    float t2= uv3[1] - uv1[1];
    float det= (s1 * t2 - s2 * t1);

    if(det != 0.0f) { /* otherwise 'tang' becomes nan */
        float tangv[3], ct[3], e1[3], e2[3];

        det= 1.0f/det;

        /* normals in render are inversed... */
        sub_v3_v3v3(e1, co1, co2);
        sub_v3_v3v3(e2, co1, co3);
        tang[0] = (t2*e1[0] - t1*e2[0])*det;
        tang[1] = (t2*e1[1] - t1*e2[1])*det;
        tang[2] = (t2*e1[2] - t1*e2[2])*det;
        tangv[0] = (s1*e2[0] - s2*e1[0])*det;
        tangv[1] = (s1*e2[1] - s2*e1[1])*det;
        tangv[2] = (s1*e2[2] - s2*e1[2])*det;
        cross_v3_v3v3(ct, tang, tangv);
    
        /* check flip */
        if ((ct[0]*n[0] + ct[1]*n[1] + ct[2]*n[2]) < 0.0f)
            negate_v3(tang);
    }
    else {
        tang[0]= tang[1]= tang[2]=  0.0;
    }
}

/****************************** Vector Clouds ********************************/

/* vector clouds */
/* void vcloud_estimate_transform(int list_size, float (*pos)[3], float *weight,float (*rpos)[3], float *rweight,
                                 float lloc[3],float rloc[3],float lrot[3][3],float lscale[3][3])

input
(
int list_size
4 lists as pointer to array[list_size]
1. current pos array of 'new' positions 
2. current weight array of 'new'weights (may be NULL pointer if you have no weights )
3. reference rpos array of 'old' positions
4. reference rweight array of 'old'weights (may be NULL pointer if you have no weights )
)
output  
(
float lloc[3] center of mass pos
float rloc[3] center of mass rpos
float lrot[3][3] rotation matrix
float lscale[3][3] scale matrix
pointers may be NULL if not needed
)

*/
/* can't believe there is none in math utils */
static float _det_m3(float m2[3][3])
{
    float det = 0.f;
    if (m2){
    det= m2[0][0]* (m2[1][1]*m2[2][2] - m2[1][2]*m2[2][1])
        -m2[1][0]* (m2[0][1]*m2[2][2] - m2[0][2]*m2[2][1])
        +m2[2][0]* (m2[0][1]*m2[1][2] - m2[0][2]*m2[1][1]);
    }
    return det;
}


void vcloud_estimate_transform(int list_size, float (*pos)[3], float *weight,float (*rpos)[3], float *rweight,
                            float lloc[3],float rloc[3],float lrot[3][3],float lscale[3][3])
{
    float accu_com[3]= {0.0f,0.0f,0.0f}, accu_rcom[3]= {0.0f,0.0f,0.0f};
    float accu_weight = 0.0f,accu_rweight = 0.0f,eps = 0.000001f;

    int a;
    /* first set up a nice default response */
    if (lloc) zero_v3(lloc);
    if (rloc) zero_v3(rloc);
    if (lrot) unit_m3(lrot);
    if (lscale) unit_m3(lscale);
    /* do com for both clouds */
    if (pos && rpos && (list_size > 0)) /* paranoya check */
    {
        /* do com for both clouds */
        for(a=0; a<list_size; a++){
            if (weight){
                float v[3];
                copy_v3_v3(v,pos[a]);
                mul_v3_fl(v,weight[a]);
                add_v3_v3(accu_com, v);
                accu_weight +=weight[a]; 
            }
            else add_v3_v3(accu_com, pos[a]);

            if (rweight){
                float v[3];
                copy_v3_v3(v,rpos[a]);
                mul_v3_fl(v,rweight[a]);
                add_v3_v3(accu_rcom, v);
                accu_rweight +=rweight[a]; 
            }
            else add_v3_v3(accu_rcom, rpos[a]);

        }
        if (!weight || !rweight){
            accu_weight = accu_rweight = list_size;
        }

        mul_v3_fl(accu_com,1.0f/accu_weight);
        mul_v3_fl(accu_rcom,1.0f/accu_rweight);
        if (lloc) copy_v3_v3(lloc,accu_com);
        if (rloc) copy_v3_v3(rloc,accu_rcom);
        if (lrot || lscale){ /* caller does not want rot nor scale, strange but legal */
            /*so now do some reverse engeneering and see if we can split rotation from scale ->Polardecompose*/
            /* build 'projection' matrix */
            float m[3][3],mr[3][3],q[3][3],qi[3][3];
            float va[3],vb[3],stunt[3];
            float odet,ndet;
            int i=0,imax=15;
            zero_m3(m);
            zero_m3(mr);

            /* build 'projection' matrix */
            for(a=0; a<list_size; a++){
                sub_v3_v3v3(va,rpos[a],accu_rcom);
                /* mul_v3_fl(va,bp->mass);  mass needs renormalzation here ?? */
                sub_v3_v3v3(vb,pos[a],accu_com);
                /* mul_v3_fl(va,rp->mass); */
                m[0][0] += va[0] * vb[0];
                m[0][1] += va[0] * vb[1];
                m[0][2] += va[0] * vb[2];

                m[1][0] += va[1] * vb[0];
                m[1][1] += va[1] * vb[1];
                m[1][2] += va[1] * vb[2];

                m[2][0] += va[2] * vb[0];
                m[2][1] += va[2] * vb[1];
                m[2][2] += va[2] * vb[2];

                /* building the referenc matrix on the fly
                needed to scale properly later*/

                mr[0][0] += va[0] * va[0];
                mr[0][1] += va[0] * va[1];
                mr[0][2] += va[0] * va[2];

                mr[1][0] += va[1] * va[0];
                mr[1][1] += va[1] * va[1];
                mr[1][2] += va[1] * va[2];

                mr[2][0] += va[2] * va[0];
                mr[2][1] += va[2] * va[1];
                mr[2][2] += va[2] * va[2];
            }
            copy_m3_m3(q,m);
            stunt[0] = q[0][0]; stunt[1] = q[1][1]; stunt[2] = q[2][2];
            /* renormalizing for numeric stability */
            mul_m3_fl(q,1.f/len_v3(stunt)); 

            /* this is pretty much Polardecompose 'inline' the algo based on Higham's thesis */
            /* without the far case ... but seems to work here pretty neat                   */
            odet = 0.f;
            ndet = _det_m3(q);
            while((odet-ndet)*(odet-ndet) > eps && i<imax){
                invert_m3_m3(qi,q);
                transpose_m3(qi);
                add_m3_m3m3(q,q,qi);
                mul_m3_fl(q,0.5f);
                odet =ndet;
                ndet =_det_m3(q);
                i++;
            }

            if (i){
                float scale[3][3];
                float irot[3][3];
                if(lrot) copy_m3_m3(lrot,q);
                invert_m3_m3(irot,q);
                invert_m3_m3(qi,mr);
                mul_m3_m3m3(q,m,qi); 
                mul_m3_m3m3(scale,irot,q); 
                if(lscale) copy_m3_m3(lscale,scale);

            }
        }
    }
}

/******************************* Form Factor *********************************/

static void vec_add_dir(float r[3], const float v1[3], const float v2[3], const float fac)
{
    r[0]= v1[0] + fac*(v2[0] - v1[0]);
    r[1]= v1[1] + fac*(v2[1] - v1[1]);
    r[2]= v1[2] + fac*(v2[2] - v1[2]);
}

static int ff_visible_quad(const float p[3], const float n[3], const float v0[3], const float v1[3], const float v2[3], float q0[3], float q1[3], float q2[3], float q3[3])
{
    static const float epsilon = 1e-6f;
    float c, sd[3];
    
    c= dot_v3v3(n, p);

    /* signed distances from the vertices to the plane. */
    sd[0]= dot_v3v3(n, v0) - c;
    sd[1]= dot_v3v3(n, v1) - c;
    sd[2]= dot_v3v3(n, v2) - c;

    if(fabsf(sd[0]) < epsilon) sd[0] = 0.0f;
    if(fabsf(sd[1]) < epsilon) sd[1] = 0.0f;
    if(fabsf(sd[2]) < epsilon) sd[2] = 0.0f;

    if(sd[0] > 0) {
        if(sd[1] > 0) {
            if(sd[2] > 0) {
                // +++
                copy_v3_v3(q0, v0);
                copy_v3_v3(q1, v1);
                copy_v3_v3(q2, v2);
                copy_v3_v3(q3, q2);
            }
            else if(sd[2] < 0) {
                // ++-
                copy_v3_v3(q0, v0);
                copy_v3_v3(q1, v1);
                vec_add_dir(q2, v1, v2, (sd[1]/(sd[1]-sd[2])));
                vec_add_dir(q3, v0, v2, (sd[0]/(sd[0]-sd[2])));
            }
            else {
                // ++0
                copy_v3_v3(q0, v0);
                copy_v3_v3(q1, v1);
                copy_v3_v3(q2, v2);
                copy_v3_v3(q3, q2);
            }
        }
        else if(sd[1] < 0) {
            if(sd[2] > 0) {
                // +-+
                copy_v3_v3(q0, v0);
                vec_add_dir(q1, v0, v1, (sd[0]/(sd[0]-sd[1])));
                vec_add_dir(q2, v1, v2, (sd[1]/(sd[1]-sd[2])));
                copy_v3_v3(q3, v2);
            }
            else if(sd[2] < 0) {
                // +--
                copy_v3_v3(q0, v0);
                vec_add_dir(q1, v0, v1, (sd[0]/(sd[0]-sd[1])));
                vec_add_dir(q2, v0, v2, (sd[0]/(sd[0]-sd[2])));
                copy_v3_v3(q3, q2);
            }
            else {
                // +-0
                copy_v3_v3(q0, v0);
                vec_add_dir(q1, v0, v1, (sd[0]/(sd[0]-sd[1])));
                copy_v3_v3(q2, v2);
                copy_v3_v3(q3, q2);
            }
        }
        else {
            if(sd[2] > 0) {
                // +0+
                copy_v3_v3(q0, v0);
                copy_v3_v3(q1, v1);
                copy_v3_v3(q2, v2);
                copy_v3_v3(q3, q2);
            }
            else if(sd[2] < 0) {
                // +0-
                copy_v3_v3(q0, v0);
                copy_v3_v3(q1, v1);
                vec_add_dir(q2, v0, v2, (sd[0]/(sd[0]-sd[2])));
                copy_v3_v3(q3, q2);
            }
            else {
                // +00
                copy_v3_v3(q0, v0);
                copy_v3_v3(q1, v1);
                copy_v3_v3(q2, v2);
                copy_v3_v3(q3, q2);
            }
        }
    }
    else if(sd[0] < 0) {
        if(sd[1] > 0) {
            if(sd[2] > 0) {
                // -++
                vec_add_dir(q0, v0, v1, (sd[0]/(sd[0]-sd[1])));
                copy_v3_v3(q1, v1);
                copy_v3_v3(q2, v2);
                vec_add_dir(q3, v0, v2, (sd[0]/(sd[0]-sd[2])));
            }
            else if(sd[2] < 0) {
                // -+-
                vec_add_dir(q0, v0, v1, (sd[0]/(sd[0]-sd[1])));
                copy_v3_v3(q1, v1);
                vec_add_dir(q2, v1, v2, (sd[1]/(sd[1]-sd[2])));
                copy_v3_v3(q3, q2);
            }
            else {
                // -+0
                vec_add_dir(q0, v0, v1, (sd[0]/(sd[0]-sd[1])));
                copy_v3_v3(q1, v1);
                copy_v3_v3(q2, v2);
                copy_v3_v3(q3, q2);
            }
        }
        else if(sd[1] < 0) {
            if(sd[2] > 0) {
                // --+
                vec_add_dir(q0, v0, v2, (sd[0]/(sd[0]-sd[2])));
                vec_add_dir(q1, v1, v2, (sd[1]/(sd[1]-sd[2])));
                copy_v3_v3(q2, v2);
                copy_v3_v3(q3, q2);
            }
            else if(sd[2] < 0) {
                // ---
                return 0;
            }
            else {
                // --0
                return 0;
            }
        }
        else {
            if(sd[2] > 0) {
                // -0+
                vec_add_dir(q0, v0, v2, (sd[0]/(sd[0]-sd[2])));
                copy_v3_v3(q1, v1);
                copy_v3_v3(q2, v2);
                copy_v3_v3(q3, q2);
            }
            else if(sd[2] < 0) {
                // -0-
                return 0;
            }
            else {
                // -00
                return 0;
            }
        }
    }
    else {
        if(sd[1] > 0) {
            if(sd[2] > 0) {
                // 0++
                copy_v3_v3(q0, v0);
                copy_v3_v3(q1, v1);
                copy_v3_v3(q2, v2);
                copy_v3_v3(q3, q2);
            }
            else if(sd[2] < 0) {
                // 0+-
                copy_v3_v3(q0, v0);
                copy_v3_v3(q1, v1);
                vec_add_dir(q2, v1, v2, (sd[1]/(sd[1]-sd[2])));
                copy_v3_v3(q3, q2);
            }
            else {
                // 0+0
                copy_v3_v3(q0, v0);
                copy_v3_v3(q1, v1);
                copy_v3_v3(q2, v2);
                copy_v3_v3(q3, q2);
            }
        }
        else if(sd[1] < 0) {
            if(sd[2] > 0) {
                // 0-+
                copy_v3_v3(q0, v0);
                vec_add_dir(q1, v1, v2, (sd[1]/(sd[1]-sd[2])));
                copy_v3_v3(q2, v2);
                copy_v3_v3(q3, q2);
            }
            else if(sd[2] < 0) {
                // 0--
                return 0;
            }
            else {
                // 0-0
                return 0;
            }
        }
        else {
            if(sd[2] > 0) {
                // 00+
                copy_v3_v3(q0, v0);
                copy_v3_v3(q1, v1);
                copy_v3_v3(q2, v2);
                copy_v3_v3(q3, q2);
            }
            else if(sd[2] < 0) {
                // 00-
                return 0;
            }
            else {
                // 000
                return 0;
            }
        }
    }

    return 1;
}

/* altivec optimization, this works, but is unused */

#if 0
#include <Accelerate/Accelerate.h>

typedef union {
    vFloat v;
    float f[4];
} vFloatResult;

static vFloat vec_splat_float(float val)
{
    return (vFloat){val, val, val, val};
}

static float ff_quad_form_factor(float *p, float *n, float *q0, float *q1, float *q2, float *q3)
{
    vFloat vcos, rlen, vrx, vry, vrz, vsrx, vsry, vsrz, gx, gy, gz, vangle;
    vUInt8 rotate = (vUInt8){4,5,6,7,8,9,10,11,12,13,14,15,0,1,2,3};
    vFloatResult vresult;
    float result;

    /* compute r* */
    vrx = (vFloat){q0[0], q1[0], q2[0], q3[0]} - vec_splat_float(p[0]);
    vry = (vFloat){q0[1], q1[1], q2[1], q3[1]} - vec_splat_float(p[1]);
    vrz = (vFloat){q0[2], q1[2], q2[2], q3[2]} - vec_splat_float(p[2]);

    /* normalize r* */
    rlen = vec_rsqrte(vrx*vrx + vry*vry + vrz*vrz + vec_splat_float(1e-16f));
    vrx = vrx*rlen;
    vry = vry*rlen;
    vrz = vrz*rlen;

    /* rotate r* for cross and dot */
    vsrx= vec_perm(vrx, vrx, rotate);
    vsry= vec_perm(vry, vry, rotate);
    vsrz= vec_perm(vrz, vrz, rotate);

    /* cross product */
    gx = vsry*vrz - vsrz*vry;
    gy = vsrz*vrx - vsrx*vrz;
    gz = vsrx*vry - vsry*vrx;

    /* normalize */
    rlen = vec_rsqrte(gx*gx + gy*gy + gz*gz + vec_splat_float(1e-16f));
    gx = gx*rlen;
    gy = gy*rlen;
    gz = gz*rlen;

    /* angle */
    vcos = vrx*vsrx + vry*vsry + vrz*vsrz;
    vcos= vec_max(vec_min(vcos, vec_splat_float(1.0f)), vec_splat_float(-1.0f));
    vangle= vacosf(vcos);

    /* dot */
    vresult.v = (vec_splat_float(n[0])*gx +
                 vec_splat_float(n[1])*gy +
                 vec_splat_float(n[2])*gz)*vangle;

    result= (vresult.f[0] + vresult.f[1] + vresult.f[2] + vresult.f[3])*(0.5f/(float)M_PI);
    result= MAX2(result, 0.0f);

    return result;
}

#endif

/* SSE optimization, acos code doesn't work */

#if 0

#include <xmmintrin.h>

static __m128 sse_approx_acos(__m128 x)
{
    /* needs a better approximation than taylor expansion of acos, since that
     * gives big erros for near 1.0 values, sqrt(2*x)*acos(1-x) should work
     * better, see http://www.tom.womack.net/projects/sse-fast-arctrig.html */

    return _mm_set_ps1(1.0f);
}

static float ff_quad_form_factor(float *p, float *n, float *q0, float *q1, float *q2, float *q3)
{
    float r0[3], r1[3], r2[3], r3[3], g0[3], g1[3], g2[3], g3[3];
    float a1, a2, a3, a4, dot1, dot2, dot3, dot4, result;
    float fresult[4] __attribute__((aligned(16)));
    __m128 qx, qy, qz, rx, ry, rz, rlen, srx, sry, srz, gx, gy, gz, glen, rcos, angle, aresult;

    /* compute r */
    qx = _mm_set_ps(q3[0], q2[0], q1[0], q0[0]);
    qy = _mm_set_ps(q3[1], q2[1], q1[1], q0[1]);
    qz = _mm_set_ps(q3[2], q2[2], q1[2], q0[2]);

    rx = qx - _mm_set_ps1(p[0]);
    ry = qy - _mm_set_ps1(p[1]);
    rz = qz - _mm_set_ps1(p[2]);

    /* normalize r */
    rlen = _mm_rsqrt_ps(rx*rx + ry*ry + rz*rz + _mm_set_ps1(1e-16f));
    rx = rx*rlen;
    ry = ry*rlen;
    rz = rz*rlen;

    /* cross product */
    srx = _mm_shuffle_ps(rx, rx, _MM_SHUFFLE(0,3,2,1));
    sry = _mm_shuffle_ps(ry, ry, _MM_SHUFFLE(0,3,2,1));
    srz = _mm_shuffle_ps(rz, rz, _MM_SHUFFLE(0,3,2,1));

    gx = sry*rz - srz*ry;
    gy = srz*rx - srx*rz;
    gz = srx*ry - sry*rx;

    /* normalize g */
    glen = _mm_rsqrt_ps(gx*gx + gy*gy + gz*gz + _mm_set_ps1(1e-16f));
    gx = gx*glen;
    gy = gy*glen;
    gz = gz*glen;

    /* compute angle */
    rcos = rx*srx + ry*sry + rz*srz;
    rcos= _mm_max_ps(_mm_min_ps(rcos, _mm_set_ps1(1.0f)), _mm_set_ps1(-1.0f));

    angle = sse_approx_cos(rcos);
    aresult = (_mm_set_ps1(n[0])*gx + _mm_set_ps1(n[1])*gy + _mm_set_ps1(n[2])*gz)*angle;

    /* sum together */
    result= (fresult[0] + fresult[1] + fresult[2] + fresult[3])*(0.5f/(float)M_PI);
    result= MAX2(result, 0.0f);

    return result;
}

#endif

static void ff_normalize(float n[3])
{
    float d;
    
    d= dot_v3v3(n, n);

    if(d > 1.0e-35F) {
        d= 1.0f/sqrtf(d);

        n[0] *= d; 
        n[1] *= d; 
        n[2] *= d;
    } 
}

static float ff_quad_form_factor(const float p[3], const float n[3], const float q0[3], const float q1[3], const float q2[3], const float q3[3])
{
    float r0[3], r1[3], r2[3], r3[3], g0[3], g1[3], g2[3], g3[3];
    float a1, a2, a3, a4, dot1, dot2, dot3, dot4, result;

    sub_v3_v3v3(r0, q0, p);
    sub_v3_v3v3(r1, q1, p);
    sub_v3_v3v3(r2, q2, p);
    sub_v3_v3v3(r3, q3, p);

    ff_normalize(r0);
    ff_normalize(r1);
    ff_normalize(r2);
    ff_normalize(r3);

    cross_v3_v3v3(g0, r1, r0); ff_normalize(g0);
    cross_v3_v3v3(g1, r2, r1); ff_normalize(g1);
    cross_v3_v3v3(g2, r3, r2); ff_normalize(g2);
    cross_v3_v3v3(g3, r0, r3); ff_normalize(g3);

    a1= saacosf(dot_v3v3(r0, r1));
    a2= saacosf(dot_v3v3(r1, r2));
    a3= saacosf(dot_v3v3(r2, r3));
    a4= saacosf(dot_v3v3(r3, r0));

    dot1= dot_v3v3(n, g0);
    dot2= dot_v3v3(n, g1);
    dot3= dot_v3v3(n, g2);
    dot4= dot_v3v3(n, g3);

    result= (a1*dot1 + a2*dot2 + a3*dot3 + a4*dot4)*0.5f/(float)M_PI;
    result= MAX2(result, 0.0f);

    return result;
}

float form_factor_hemi_poly(float p[3], float n[3], float v1[3], float v2[3], float v3[3], float v4[3])
{
    /* computes how much hemisphere defined by point and normal is
       covered by a quad or triangle, cosine weighted */
    float q0[3], q1[3], q2[3], q3[3], contrib= 0.0f;

    if(ff_visible_quad(p, n, v1, v2, v3, q0, q1, q2, q3))
        contrib += ff_quad_form_factor(p, n, q0, q1, q2, q3);
    
    if(v4 && ff_visible_quad(p, n, v1, v3, v4, q0, q1, q2, q3))
        contrib += ff_quad_form_factor(p, n, q0, q1, q2, q3);

    return contrib;
}