void Polygon::Compute_Polygon(int number, Vector3d *points) { int i; DBL x, y, z, d; Vector3d o, u, v, w, N; MATRIX a, b; /* Create polygon data. */ if (Data == NULL) { Data = reinterpret_cast<POLYGON_DATA *>(POV_MALLOC(sizeof(POLYGON_DATA), "polygon points")); Data->References = 1; Data->Number = number; Data->Points = reinterpret_cast<Vector2d *>(POV_MALLOC(number*sizeof(Vector2d), "polygon points")); } else { throw POV_EXCEPTION_STRING("Polygon data already computed."); } /* Get polygon's coordinate system (one of the many possible) */ o = points[0]; /* Find valid, i.e. non-zero u vector. */ for (i = 1; i < number; i++) { u = points[i] - o; if (u.lengthSqr() > EPSILON) { break; } } if (i == number) { Set_Flag(this, DEGENERATE_FLAG); ;// TODO MESSAGE Warning("Points in polygon are co-linear. Ignoring polygon."); } /* Find valid, i.e. non-zero v and w vectors. */ for (i++; i < number; i++) { v = points[i] - o; w = cross(u, v); if ((v.lengthSqr() > EPSILON) && (w.lengthSqr() > EPSILON)) { break; } } if (i == number) { Set_Flag(this, DEGENERATE_FLAG); ;// TODO MESSAGE Warning("Points in polygon are co-linear. Ignoring polygon."); } u = cross(v, w); v = cross(w, u); u.normalize(); v.normalize(); w.normalize(); MIdentity(a); MIdentity(b); a[3][0] = -o[X]; a[3][1] = -o[Y]; a[3][2] = -o[Z]; b[0][0] = u[X]; b[1][0] = u[Y]; b[2][0] = u[Z]; b[0][1] = v[X]; b[1][1] = v[Y]; b[2][1] = v[Z]; b[0][2] = w[X]; b[1][2] = w[Y]; b[2][2] = w[Z]; MTimesC(Trans->inverse, a, b); MInvers(Trans->matrix, Trans->inverse); /* Project points onto the u,v-plane (3D --> 2D) */ for (i = 0; i < number; i++) { x = points[i][X] - o[X]; y = points[i][Y] - o[Y]; z = points[i][Z] - o[Z]; d = x * w[X] + y * w[Y] + z * w[Z]; if (fabs(d) > ZERO_TOLERANCE) { Set_Flag(this, DEGENERATE_FLAG); ;// TODO MESSAGE Warning("Points in polygon are not co-planar. Ignoring polygons."); } Data->Points[i][X] = x * u[X] + y * u[Y] + z * u[Z]; Data->Points[i][Y] = x * v[X] + y * v[Y] + z * v[Z]; } N = Vector3d(0.0, 0.0, 1.0); MTransNormal(S_Normal, N, Trans); S_Normal.normalize(); Compute_BBox(); }
void Compute_Polygon(POLYGON *Polyg, int Number, VECTOR *Points) { int i; DBL x, y, z, d; VECTOR o, u, v, w, N; MATRIX a, b; /* Create polygon data. */ if (Polyg->Data == NULL) { Polyg->Data = (POLYGON_DATA *)POV_MALLOC(sizeof(POLYGON_DATA), "polygon points"); Polyg->Data->References = 1; Polyg->Data->Number = Number; Polyg->Data->Points = (UV_VECT *)POV_MALLOC(Number*sizeof(UV_VECT), "polygon points"); } else { Error("Polygon data already computed."); } /* Get polygon's coordinate system (one of the many possible) */ Assign_Vector(o, Points[0]); /* Find valid, i.e. non-zero u vector. */ for (i = 1; i < Number; i++) { VSub(u, Points[i], o); if (VSumSqr(u) > EPSILON) { break; } } if (i == Number) { Set_Flag(Polyg, DEGENERATE_FLAG); Warning(0, "Points in polygon are co-linear. Ignoring polygon."); } /* Find valid, i.e. non-zero v and w vectors. */ for (i++; i < Number; i++) { VSub(v, Points[i], o); VCross(w, u, v); if ((VSumSqr(v) > EPSILON) && (VSumSqr(w) > EPSILON)) { break; } } if (i == Number) { Set_Flag(Polyg, DEGENERATE_FLAG); Warning(0, "Points in polygon are co-linear. Ignoring polygon."); } VCross(u, v, w); VCross(v, w, u); VNormalize(u, u); VNormalize(v, v); VNormalize(w, w); MIdentity(a); MIdentity(b); a[3][0] = -o[X]; a[3][1] = -o[Y]; a[3][2] = -o[Z]; b[0][0] = u[X]; b[1][0] = u[Y]; b[2][0] = u[Z]; b[0][1] = v[X]; b[1][1] = v[Y]; b[2][1] = v[Z]; b[0][2] = w[X]; b[1][2] = w[Y]; b[2][2] = w[Z]; MTimesC(Polyg->Trans->inverse, a, b); MInvers(Polyg->Trans->matrix, Polyg->Trans->inverse); /* Project points onto the u,v-plane (3D --> 2D) */ for (i = 0; i < Number; i++) { x = Points[i][X] - o[X]; y = Points[i][Y] - o[Y]; z = Points[i][Z] - o[Z]; d = x * w[X] + y * w[Y] + z * w[Z]; if (fabs(d) > ZERO_TOLERANCE) { Set_Flag(Polyg, DEGENERATE_FLAG); Warning(0, "Points in polygon are not co-planar. Ignoring polygons."); } Polyg->Data->Points[i][X] = x * u[X] + y * u[Y] + z * u[Z]; Polyg->Data->Points[i][Y] = x * v[X] + y * v[Y] + z * v[Z]; } Make_Vector(N, 0.0, 0.0, 1.0); MTransNormal(Polyg->S_Normal, N, Polyg->Trans); VNormalizeEq(Polyg->S_Normal); Compute_Polygon_BBox(Polyg); }