1 /* 2 * Copyright 2012 Google Inc. 3 * 4 * Use of this source code is governed by a BSD-style license that can be 5 * found in the LICENSE file. 6 */ 7 #include "CurveIntersection.h" 8 #include "IntersectionUtilities.h" 9 #include "QuadraticUtilities.h" 10 11 /* 12 Given a quadratic q, t1, and t2, find a small quadratic segment. 13 14 The new quadratic is defined by A, B, and C, where 15 A = c[0]*(1 - t1)*(1 - t1) + 2*c[1]*t1*(1 - t1) + c[2]*t1*t1 16 C = c[3]*(1 - t1)*(1 - t1) + 2*c[2]*t1*(1 - t1) + c[1]*t1*t1 17 18 To find B, compute the point halfway between t1 and t2: 19 20 q(at (t1 + t2)/2) == D 21 22 Next, compute where D must be if we know the value of B: 23 24 _12 = A/2 + B/2 25 12_ = B/2 + C/2 26 123 = A/4 + B/2 + C/4 27 = D 28 29 Group the known values on one side: 30 31 B = D*2 - A/2 - C/2 32 */ 33 34 static double interp_quad_coords(const double* src, double t) 35 { 36 double ab = interp(src[0], src[2], t); 37 double bc = interp(src[2], src[4], t); 38 double abc = interp(ab, bc, t); 39 return abc; 40 } 41 42 void sub_divide(const Quadratic& src, double t1, double t2, Quadratic& dst) { 43 double ax = dst[0].x = interp_quad_coords(&src[0].x, t1); 44 double ay = dst[0].y = interp_quad_coords(&src[0].y, t1); 45 double dx = interp_quad_coords(&src[0].x, (t1 + t2) / 2); 46 double dy = interp_quad_coords(&src[0].y, (t1 + t2) / 2); 47 double cx = dst[2].x = interp_quad_coords(&src[0].x, t2); 48 double cy = dst[2].y = interp_quad_coords(&src[0].y, t2); 49 /* bx = */ dst[1].x = 2*dx - (ax + cx)/2; 50 /* by = */ dst[1].y = 2*dy - (ay + cy)/2; 51 } 52 53 _Point sub_divide(const Quadratic& src, const _Point& a, const _Point& c, double t1, double t2) { 54 _Point b; 55 double dx = interp_quad_coords(&src[0].x, (t1 + t2) / 2); 56 double dy = interp_quad_coords(&src[0].y, (t1 + t2) / 2); 57 b.x = 2 * dx - (a.x + c.x) / 2; 58 b.y = 2 * dy - (a.y + c.y) / 2; 59 return b; 60 } 61 62 /* classic one t subdivision */ 63 static void interp_quad_coords(const double* src, double* dst, double t) 64 { 65 double ab = interp(src[0], src[2], t); 66 double bc = interp(src[2], src[4], t); 67 68 dst[0] = src[0]; 69 dst[2] = ab; 70 dst[4] = interp(ab, bc, t); 71 dst[6] = bc; 72 dst[8] = src[4]; 73 } 74 75 void chop_at(const Quadratic& src, QuadraticPair& dst, double t) 76 { 77 interp_quad_coords(&src[0].x, &dst.pts[0].x, t); 78 interp_quad_coords(&src[0].y, &dst.pts[0].y, t); 79 } 80
