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 "DataTypes.h"
8
9// Sources
10// computer-aided design - volume 22 number 9 november 1990 pp 538 - 549
11// online at http://cagd.cs.byu.edu/~tom/papers/bezclip.pdf
12
13// This turns a line segment into a parameterized line, of the form
14// ax + by + c = 0
15// When a^2 + b^2 == 1, the line is normalized.
16// The distance to the line for (x, y) is d(x,y) = ax + by + c
17//
18// Note that the distances below are not necessarily normalized. To get the true
19// distance, it's necessary to either call normalize() after xxxEndPoints(), or
20// divide the result of xxxDistance() by sqrt(normalSquared())
21
22class LineParameters {
23public:
24    void cubicEndPoints(const Cubic& pts) {
25        cubicEndPoints(pts, 0, 3);
26    }
27
28    void cubicEndPoints(const Cubic& pts, int s, int e) {
29        a = approximately_pin(pts[s].y - pts[e].y);
30        b = approximately_pin(pts[e].x - pts[s].x);
31        c = pts[s].x * pts[e].y - pts[e].x * pts[s].y;
32    }
33
34    void lineEndPoints(const _Line& pts) {
35        a = approximately_pin(pts[0].y - pts[1].y);
36        b = approximately_pin(pts[1].x - pts[0].x);
37        c = pts[0].x * pts[1].y - pts[1].x * pts[0].y;
38    }
39
40    void quadEndPoints(const Quadratic& pts) {
41        quadEndPoints(pts, 0, 2);
42    }
43
44    void quadEndPoints(const Quadratic& pts, int s, int e) {
45        a = approximately_pin(pts[s].y - pts[e].y);
46        b = approximately_pin(pts[e].x - pts[s].x);
47        c = pts[s].x * pts[e].y - pts[e].x * pts[s].y;
48    }
49
50    double normalSquared() const {
51        return a * a + b * b;
52    }
53
54    bool normalize() {
55        double normal = sqrt(normalSquared());
56        if (approximately_zero(normal)) {
57            a = b = c = 0;
58            return false;
59        }
60        double reciprocal = 1 / normal;
61        a *= reciprocal;
62        b *= reciprocal;
63        c *= reciprocal;
64        return true;
65    }
66
67    void cubicDistanceY(const Cubic& pts, Cubic& distance) const {
68        double oneThird = 1 / 3.0;
69        for (int index = 0; index < 4; ++index) {
70            distance[index].x = index * oneThird;
71            distance[index].y = a * pts[index].x + b * pts[index].y + c;
72        }
73    }
74
75    void quadDistanceY(const Quadratic& pts, Quadratic& distance) const {
76        double oneHalf = 1 / 2.0;
77        for (int index = 0; index < 3; ++index) {
78            distance[index].x = index * oneHalf;
79            distance[index].y = a * pts[index].x + b * pts[index].y + c;
80        }
81    }
82
83    double controlPtDistance(const Cubic& pts, int index) const {
84        SkASSERT(index == 1 || index == 2);
85        return a * pts[index].x + b * pts[index].y + c;
86    }
87
88    double controlPtDistance(const Quadratic& pts) const {
89        return a * pts[1].x + b * pts[1].y + c;
90    }
91
92    double pointDistance(const _Point& pt) const {
93        return a * pt.x + b * pt.y + c;
94    }
95
96    double dx() const {
97        return b;
98    }
99
100    double dy() const {
101        return -a;
102    }
103
104private:
105    double a;
106    double b;
107    double c;
108};
109