c83c70e911
git-svn-id: http://skia.googlecode.com/svn/trunk@7836 2bbb7eff-a529-9590-31e7-b0007b416f81
80 lines
2.3 KiB
C++
80 lines
2.3 KiB
C++
/*
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* Copyright 2012 Google Inc.
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*
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* Use of this source code is governed by a BSD-style license that can be
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* found in the LICENSE file.
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*/
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#include "CurveIntersection.h"
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#include "IntersectionUtilities.h"
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#include "QuadraticUtilities.h"
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/*
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Given a quadratic q, t1, and t2, find a small quadratic segment.
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The new quadratic is defined by A, B, and C, where
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A = c[0]*(1 - t1)*(1 - t1) + 2*c[1]*t1*(1 - t1) + c[2]*t1*t1
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C = c[3]*(1 - t1)*(1 - t1) + 2*c[2]*t1*(1 - t1) + c[1]*t1*t1
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To find B, compute the point halfway between t1 and t2:
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q(at (t1 + t2)/2) == D
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Next, compute where D must be if we know the value of B:
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_12 = A/2 + B/2
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12_ = B/2 + C/2
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123 = A/4 + B/2 + C/4
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= D
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Group the known values on one side:
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B = D*2 - A/2 - C/2
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*/
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static double interp_quad_coords(const double* src, double t)
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{
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double ab = interp(src[0], src[2], t);
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double bc = interp(src[2], src[4], t);
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double abc = interp(ab, bc, t);
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return abc;
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}
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void sub_divide(const Quadratic& src, double t1, double t2, Quadratic& dst) {
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double ax = dst[0].x = interp_quad_coords(&src[0].x, t1);
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double ay = dst[0].y = interp_quad_coords(&src[0].y, t1);
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double dx = interp_quad_coords(&src[0].x, (t1 + t2) / 2);
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double dy = interp_quad_coords(&src[0].y, (t1 + t2) / 2);
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double cx = dst[2].x = interp_quad_coords(&src[0].x, t2);
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double cy = dst[2].y = interp_quad_coords(&src[0].y, t2);
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/* bx = */ dst[1].x = 2*dx - (ax + cx)/2;
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/* by = */ dst[1].y = 2*dy - (ay + cy)/2;
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}
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_Point sub_divide(const Quadratic& src, const _Point& a, const _Point& c, double t1, double t2) {
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_Point b;
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double dx = interp_quad_coords(&src[0].x, (t1 + t2) / 2);
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double dy = interp_quad_coords(&src[0].y, (t1 + t2) / 2);
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b.x = 2 * dx - (a.x + c.x) / 2;
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b.y = 2 * dy - (a.y + c.y) / 2;
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return b;
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}
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/* classic one t subdivision */
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static void interp_quad_coords(const double* src, double* dst, double t)
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{
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double ab = interp(src[0], src[2], t);
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double bc = interp(src[2], src[4], t);
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dst[0] = src[0];
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dst[2] = ab;
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dst[4] = interp(ab, bc, t);
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dst[6] = bc;
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dst[8] = src[4];
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}
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void chop_at(const Quadratic& src, QuadraticPair& dst, double t)
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{
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interp_quad_coords(&src[0].x, &dst.pts[0].x, t);
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interp_quad_coords(&src[0].y, &dst.pts[0].y, t);
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}
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