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 "SkPathOpsLine.h"
8
9 // may have this below somewhere else already:
10 // copying here because I thought it was clever
11
12 // Copyright 2001, softSurfer (www.softsurfer.com)
13 // This code may be freely used and modified for any purpose
14 // providing that this copyright notice is included with it.
15 // SoftSurfer makes no warranty for this code, and cannot be held
16 // liable for any real or imagined damage resulting from its use.
17 // Users of this code must verify correctness for their application.
18
19 // Assume that a class is already given for the object:
20 // Point with coordinates {float x, y;}
21 //===================================================================
22
23 // (only used by testing)
24 // isLeft(): tests if a point is Left|On|Right of an infinite line.
25 // Input: three points P0, P1, and P2
26 // Return: >0 for P2 left of the line through P0 and P1
27 // =0 for P2 on the line
28 // <0 for P2 right of the line
29 // See: the January 2001 Algorithm on Area of Triangles
30 // return (float) ((P1.x - P0.x)*(P2.y - P0.y) - (P2.x - P0.x)*(P1.y - P0.y));
isLeft(const SkDPoint & pt) const31 double SkDLine::isLeft(const SkDPoint& pt) const {
32 SkDVector p0 = fPts[1] - fPts[0];
33 SkDVector p2 = pt - fPts[0];
34 return p0.cross(p2);
35 }
36
ptAtT(double t) const37 SkDPoint SkDLine::ptAtT(double t) const {
38 if (0 == t) {
39 return fPts[0];
40 }
41 if (1 == t) {
42 return fPts[1];
43 }
44 double one_t = 1 - t;
45 SkDPoint result = { one_t * fPts[0].fX + t * fPts[1].fX, one_t * fPts[0].fY + t * fPts[1].fY };
46 return result;
47 }
48
exactPoint(const SkDPoint & xy) const49 double SkDLine::exactPoint(const SkDPoint& xy) const {
50 if (xy == fPts[0]) { // do cheapest test first
51 return 0;
52 }
53 if (xy == fPts[1]) {
54 return 1;
55 }
56 return -1;
57 }
58
nearPoint(const SkDPoint & xy,bool * unequal) const59 double SkDLine::nearPoint(const SkDPoint& xy, bool* unequal) const {
60 if (!AlmostBetweenUlps(fPts[0].fX, xy.fX, fPts[1].fX)
61 || !AlmostBetweenUlps(fPts[0].fY, xy.fY, fPts[1].fY)) {
62 return -1;
63 }
64 // project a perpendicular ray from the point to the line; find the T on the line
65 SkDVector len = fPts[1] - fPts[0]; // the x/y magnitudes of the line
66 double denom = len.fX * len.fX + len.fY * len.fY; // see DLine intersectRay
67 SkDVector ab0 = xy - fPts[0];
68 double numer = len.fX * ab0.fX + ab0.fY * len.fY;
69 if (!between(0, numer, denom)) {
70 return -1;
71 }
72 double t = numer / denom;
73 SkDPoint realPt = ptAtT(t);
74 double dist = realPt.distance(xy); // OPTIMIZATION: can we compare against distSq instead ?
75 // find the ordinal in the original line with the largest unsigned exponent
76 double tiniest = SkTMin(SkTMin(SkTMin(fPts[0].fX, fPts[0].fY), fPts[1].fX), fPts[1].fY);
77 double largest = SkTMax(SkTMax(SkTMax(fPts[0].fX, fPts[0].fY), fPts[1].fX), fPts[1].fY);
78 largest = SkTMax(largest, -tiniest);
79 if (!AlmostEqualUlps(largest, largest + dist)) { // is the dist within ULPS tolerance?
80 return -1;
81 }
82 if (unequal) {
83 *unequal = (float) largest != (float) (largest + dist);
84 }
85 t = SkPinT(t); // a looser pin breaks skpwww_lptemp_com_3
86 SkASSERT(between(0, t, 1));
87 return t;
88 }
89
nearRay(const SkDPoint & xy) const90 bool SkDLine::nearRay(const SkDPoint& xy) const {
91 // project a perpendicular ray from the point to the line; find the T on the line
92 SkDVector len = fPts[1] - fPts[0]; // the x/y magnitudes of the line
93 double denom = len.fX * len.fX + len.fY * len.fY; // see DLine intersectRay
94 SkDVector ab0 = xy - fPts[0];
95 double numer = len.fX * ab0.fX + ab0.fY * len.fY;
96 double t = numer / denom;
97 SkDPoint realPt = ptAtT(t);
98 double dist = realPt.distance(xy); // OPTIMIZATION: can we compare against distSq instead ?
99 // find the ordinal in the original line with the largest unsigned exponent
100 double tiniest = SkTMin(SkTMin(SkTMin(fPts[0].fX, fPts[0].fY), fPts[1].fX), fPts[1].fY);
101 double largest = SkTMax(SkTMax(SkTMax(fPts[0].fX, fPts[0].fY), fPts[1].fX), fPts[1].fY);
102 largest = SkTMax(largest, -tiniest);
103 return RoughlyEqualUlps(largest, largest + dist); // is the dist within ULPS tolerance?
104 }
105
ExactPointH(const SkDPoint & xy,double left,double right,double y)106 double SkDLine::ExactPointH(const SkDPoint& xy, double left, double right, double y) {
107 if (xy.fY == y) {
108 if (xy.fX == left) {
109 return 0;
110 }
111 if (xy.fX == right) {
112 return 1;
113 }
114 }
115 return -1;
116 }
117
NearPointH(const SkDPoint & xy,double left,double right,double y)118 double SkDLine::NearPointH(const SkDPoint& xy, double left, double right, double y) {
119 if (!AlmostBequalUlps(xy.fY, y)) {
120 return -1;
121 }
122 if (!AlmostBetweenUlps(left, xy.fX, right)) {
123 return -1;
124 }
125 double t = (xy.fX - left) / (right - left);
126 t = SkPinT(t);
127 SkASSERT(between(0, t, 1));
128 double realPtX = (1 - t) * left + t * right;
129 SkDVector distU = {xy.fY - y, xy.fX - realPtX};
130 double distSq = distU.fX * distU.fX + distU.fY * distU.fY;
131 double dist = sqrt(distSq); // OPTIMIZATION: can we compare against distSq instead ?
132 double tiniest = SkTMin(SkTMin(y, left), right);
133 double largest = SkTMax(SkTMax(y, left), right);
134 largest = SkTMax(largest, -tiniest);
135 if (!AlmostEqualUlps(largest, largest + dist)) { // is the dist within ULPS tolerance?
136 return -1;
137 }
138 return t;
139 }
140
ExactPointV(const SkDPoint & xy,double top,double bottom,double x)141 double SkDLine::ExactPointV(const SkDPoint& xy, double top, double bottom, double x) {
142 if (xy.fX == x) {
143 if (xy.fY == top) {
144 return 0;
145 }
146 if (xy.fY == bottom) {
147 return 1;
148 }
149 }
150 return -1;
151 }
152
NearPointV(const SkDPoint & xy,double top,double bottom,double x)153 double SkDLine::NearPointV(const SkDPoint& xy, double top, double bottom, double x) {
154 if (!AlmostBequalUlps(xy.fX, x)) {
155 return -1;
156 }
157 if (!AlmostBetweenUlps(top, xy.fY, bottom)) {
158 return -1;
159 }
160 double t = (xy.fY - top) / (bottom - top);
161 t = SkPinT(t);
162 SkASSERT(between(0, t, 1));
163 double realPtY = (1 - t) * top + t * bottom;
164 SkDVector distU = {xy.fX - x, xy.fY - realPtY};
165 double distSq = distU.fX * distU.fX + distU.fY * distU.fY;
166 double dist = sqrt(distSq); // OPTIMIZATION: can we compare against distSq instead ?
167 double tiniest = SkTMin(SkTMin(x, top), bottom);
168 double largest = SkTMax(SkTMax(x, top), bottom);
169 largest = SkTMax(largest, -tiniest);
170 if (!AlmostEqualUlps(largest, largest + dist)) { // is the dist within ULPS tolerance?
171 return -1;
172 }
173 return t;
174 }
175