diff options
Diffstat (limited to 'source/blender/blenlib/intern/math_geom.c')
| -rw-r--r-- | source/blender/blenlib/intern/math_geom.c | 74 |
1 files changed, 74 insertions, 0 deletions
diff --git a/source/blender/blenlib/intern/math_geom.c b/source/blender/blenlib/intern/math_geom.c index 5979a24c807..96ed788a49f 100644 --- a/source/blender/blenlib/intern/math_geom.c +++ b/source/blender/blenlib/intern/math_geom.c @@ -1809,6 +1809,80 @@ void interp_cubic_v3(float x[3], float v[3], const float x1[3], const float v1[3 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 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]}; + + uv[0]= (float)((d*x[0] - b*x[1])/det); + uv[1]= (float)(((-c)*x[0] + a*x[1])/det); + } else zero_v2(uv); +} + +/* bilinear reverse */ +void resolve_quad_uv(float 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(uv); + + if(IS_ZERO(denom)!=0) { + const double fDen= a-fC; + if(IS_ZERO(fDen)==0) + 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; + + 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-uv[0])*(st0[0]-st3[0]) + uv[0]*(st1[0]-st2[0]); + const double denom_t= (1-uv[0])*(st0[1]-st3[1]) + 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) + uv[1]= (float) (( (1-uv[0])*(st0[i]-st[i]) + 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) |