-
Notifications
You must be signed in to change notification settings - Fork 0
/
PolygonParticle.m
294 lines (256 loc) · 12.8 KB
/
PolygonParticle.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
//
// PolygonParticle.m
// ModeMaker
//
// Created by David Hirsch on 9/24/09.
// Copyright 2009 Western Washington University. All rights reserved.
//
#import "PolygonParticle.h"
#import "constants.h"
@implementation PolygonParticle
- (id) initWithBoundsRect: (NSRect) boundsRect
size: (float) inSize
sizeSD: (float) inSizeSD
aspectRatio: (float) inAspectRatio
aspectRatioSD: (float) inAspectRatioSD
complexity: (short) inComplexity
complexitySD: (float) inComplexitySD
fabricStrength: (float) inFabricStrength
allowReentrants: (BOOL) inAllowReentrants
{
[super initWithBoundsRect:boundsRect
size: inSize
sizeSD: inSizeSD
aspectRatio: inAspectRatio
aspectRatioSD: inAspectRatioSD
complexity : inComplexity
complexitySD : inComplexitySD
fabricStrength: inFabricStrength
allowReentrants : inAllowReentrants ];
pathIsAtCenter = NO;
rotation = (pi * (1-inFabricStrength) * (float) rand() / (float) RAND_MAX) - (0.5 * pi * (1-inFabricStrength));
[self adaptToSizeWithAspectRatio: inAspectRatio
aspectRatioStdDev: inAspectRatioSD
complexity: inComplexity
complexitySD: inComplexitySD
allowReentrants: inAllowReentrants]; // this is where we set the edge lengths
return self;
}
- (BOOL) overlapsWith: (Particle *) inOtherParticle {
// quick check to see if our bounding boxes intersect
NSRect myBoundsRect = [myPath bounds];
NSRect otherBoundsRect = [[inOtherParticle path] bounds];
NSRect intersection = NSIntersectionRect(myBoundsRect, otherBoundsRect);
if (intersection.size.width == 0 && intersection.size.height == 0)
return NO;
// Now see if any of my line segments intersect any of the other's line segments
// First, extract the points into arrays for fast access:
NSBezierPath *otherPath = [inOtherParticle path];
NSPoint points[3];
NSPoint myPts[kMaxNumPolygonPoints];
NSPoint otherPts[kMaxNumPolygonPoints];
short myNumPts = 0;
short otherNumPts = 0;
for (short i = 0; i < [myPath elementCount]; i++) {
NSBezierPathElement element = [myPath elementAtIndex: i associatedPoints: points];
if (element == NSLineToBezierPathElement) {
myPts[myNumPts++] = points[0];
}
}
for (short i = 0; i < [otherPath elementCount]; i++) {
NSBezierPathElement element = [otherPath elementAtIndex: i associatedPoints: points];
if (element == NSLineToBezierPathElement) {
otherPts[otherNumPts++] = points[0];
}
}
// Now we have the points extracted, so loop through both paths, comparing all line segments. If any intersect, then we overlap
for (short myPtNum = 0; myPtNum < myNumPts; myPtNum++) {
NSPoint myCurPt = myPts[myPtNum];
NSPoint myNextPt = myPts[(myPtNum < myNumPts-1) ? myPtNum+1 : 0];
for (short otherPtNum = 0; otherPtNum < otherNumPts; otherPtNum++) {
NSPoint otherCurPt = otherPts[otherPtNum];
NSPoint otherNextPt = otherPts[(otherPtNum < otherNumPts-1) ? otherPtNum+1 : 0];
// now we test for intersection. Math from: http://local.wasp.uwa.edu.au/~pbourke/geometry/lineline2d/
// Pts 1&2 are myCurPt and myNextPt; Pts 3&4 are otherCurPt and otherNextPt
float denom = (otherNextPt.y - otherCurPt.y) * (myNextPt.x - myCurPt.x) - (otherNextPt.x - otherCurPt.x) * (myNextPt.y - myCurPt.y);
if (denom == 0) {
// then lines are parallel and do not intersect
continue;
} else {
// lines intersect, but perhaps not these line segments.
float ua = ((otherNextPt.x - otherCurPt.x) * (myCurPt.y - otherCurPt.y) - (otherNextPt.y - otherCurPt.y) * (myCurPt.x - otherCurPt.x)) / denom;
float ub = ((myNextPt.x - myCurPt.x) * (myCurPt.y - otherCurPt.y) - (myNextPt.y - myCurPt.y) * (myCurPt.x - otherCurPt.x)) / denom;
if (ua > 0 && ua < 1 && ub > 0 && ub < 1) {
// then the line segments intersect!
return YES;
}
}
}
}
return NO; // no overlap
}
- (void) adaptToSizeWithAspectRatio: (float) inAspectRatio
aspectRatioStdDev: (float) inAspectRatioStdDev
complexity: (short) inComplexity
complexitySD: (float) inComplexitySD
allowReentrants: (BOOL) inAllowReentrants {
float myAR = [self normalValueWithMean: inAspectRatio standardDev: inAspectRatioStdDev];
myAR = (myAR < kSmallestAspectRatio) ? kSmallestAspectRatio : myAR;
short myNumPoints = round( [self normalValueWithMean: inComplexity standardDev: inComplexitySD]);
myNumPoints = (myNumPoints < 3) ? 3 : myNumPoints; // must have at least 3 points in polygon
myNumPoints = (myNumPoints > kMaxNumPolygonPoints) ? kMaxNumPolygonPoints : myNumPoints;
// Note that the NumberFormatter restricts ARs to the range [1,100]
// need to make the rough polygon by dividing space into myNumPoints points around the center, then randomly
// creating vertices radially along complexity evenly-spaced lines (or perhaps not-so-evenly: use mean /SD to get some variation)
// then check for reentrants and move points outwards as needed
// then resize to achieve aspect ratio
// then resize to achieve correct area
float idealAngularDivision = 2 * pi / (float)myNumPoints;
float initialOffset = (pi * (float) rand() / (float) RAND_MAX); // offset so that we don't have a point at zero degrees in all polygons
float angleSD = idealAngularDivision * 0.1;
float defaultRadius = 10; // this is arbitrary, but the value doesn't really matter since we'll be shrinking/growing the shape to make its
// area be correct, anyway.
float radiusSD = 2;
PolarPoint polarPoints[kMaxNumPolygonPoints];
for (short thisPointNum = 0; thisPointNum < myNumPoints; thisPointNum++) { // for each point
// figure out the angle
polarPoints[thisPointNum].angle = fmod(initialOffset + (thisPointNum * idealAngularDivision) + [self normalValueWithMean: (idealAngularDivision)
standardDev: angleSD], 2.0*pi);
// figure out the radius
polarPoints[thisPointNum].radius = [self normalValueWithMean: defaultRadius
standardDev: radiusSD];
polarPoints[thisPointNum].radius = (polarPoints[thisPointNum].radius < 1) ? 1 : polarPoints[thisPointNum].radius; // radius mst be at least 1
}
PolarPoint thisPoint, prevPoint, nextPoint;
// Now we have a shape. We need to fix reentrants, if they are not allowed
if (!inAllowReentrants && myNumPoints > 3) { // can't have reentrants in a triangle
for (short thisPointNum = 0; thisPointNum < myNumPoints; thisPointNum++) { // for each point
thisPoint = polarPoints[thisPointNum];
prevPoint = polarPoints[(thisPointNum+myNumPoints-1) % myNumPoints];
nextPoint = polarPoints[(thisPointNum+1) % myNumPoints];
if (!(thisPoint.radius > prevPoint.radius && thisPoint.radius > nextPoint.radius)) { // do a quick check to see if we are clearly not reentrant
// we are not obviously safe, so calculate the minimum radius that is not reentrant
// this is inscrutable trig stuff, but I think it's correct:
float angleBefore = thisPoint.angle - prevPoint.angle;
float angleAfter = nextPoint.angle - thisPoint.angle;
float totalAngle = angleBefore + angleAfter; // this is the angle made by (the line from the center to the previous point)
// and (the line from the center to the next point)
if (totalAngle < pi) {
// can't have reentrants if the total angle is greater than 180°
/* this doesn't seem to work; I think I derived it wrong
// angleB is the angle made by (the line from the center to the previous point) and (the line from the previous
// point to the next point)
float angleB = asin(nextPoint.radius * sin(totalAngle) / prevPoint.radius);
float rMin = (prevPoint.radius * cos(angleB)) / (1.0 - (0.5 * sin(2 * totalAngle) / sin(angleB)));
if (thisPoint.radius < (rMin)) {
// we have a reentrant. If we just made r=rMin, then it would be as if this point did not exist.
// So, we'll select randomly within a safe interval (up to lesser of the two adjacent radii)
// Any greater, and we might have a chance of causing an adjacent point to BECOME reentrant
float maxSafeRadius = (prevPoint.radius < nextPoint.radius) ? prevPoint.radius : nextPoint.radius;
thisPoint.radius = ((maxSafeRadius - rMin) * (float) rand() / (float) RAND_MAX) + rMin;
}
*/
// new method:
// h is the cartesian distance from prevPoint to nextPoint. Uses Law of Cosines. Could translate into Cartesian and get vector distance, but this is probably faster
float h = sqrt(nextPoint.radius * nextPoint.radius + prevPoint.radius * prevPoint.radius - 2.0 * nextPoint.radius * prevPoint.radius * cos(totalAngle));
// delta is the angle made by (the line from the center to the previous point) and (the line from the previous
// point to the next point)
float delta = asin(nextPoint.radius * sin(totalAngle) / h);
// epsilon is the angle made by (the line from the center to the next point) and (the line from the previous
// point to the next point)
float epsilon = pi - angleBefore - delta;
float rMin = prevPoint.radius * sin(delta) / sin(epsilon);
if (thisPoint.radius < (rMin)) {
// we have a reentrant. If we just made r=rMin, then it would be as if this point did not exist.
// So, we'll select randomly within a safe interval (up to lesser of the two adjacent radii)
// Any greater, and we might have a chance of causing an adjacent point to BECOME reentrant
float maxSafeRadius = (prevPoint.radius < nextPoint.radius) ? prevPoint.radius : nextPoint.radius;
thisPoint.radius = ((maxSafeRadius - rMin) * (float) rand() / (float) RAND_MAX) + rMin;
polarPoints[thisPointNum] = thisPoint;
}
}
}
}
}
// We now have a good shape that, if desired, is not reentrant
// make the cartesian path from the polar points
[myPath removeAllPoints];
NSPoint curPoint;
NSPoint firstPoint;
for (short thisPoint = 0; thisPoint < myNumPoints; thisPoint++) { // for each point
curPoint.x = polarPoints[thisPoint].radius * cos(polarPoints[thisPoint].angle);
curPoint.y = polarPoints[thisPoint].radius * sin(polarPoints[thisPoint].angle);
if (thisPoint==0) {
[myPath moveToPoint: curPoint];
firstPoint = curPoint;
} else {
[myPath lineToPoint: curPoint];
}
}
[myPath lineToPoint:firstPoint];
[myPath closePath];
NSAffineTransform *transform = [NSAffineTransform transform];
// The current aspect ratio should be close to 1; stretch the shape
[transform scaleXBy:myAR yBy:1];
[myPath transformUsingAffineTransform: transform];
transform = [NSAffineTransform transform]; // get a new empty transform; avoids worrying about combinatory surprises
float currentArea = [self pathArea];
float scaleFactor = sqrt(area / currentArea); // need the square root since we are scaling in two directions
[transform scaleXBy:scaleFactor yBy:scaleFactor];
[myPath transformUsingAffineTransform: transform];
transform = [NSAffineTransform transform]; // get a new empty transform; avoids worrying about combinatory surprises
[transform translateXBy: center.x yBy:center.y];
[transform rotateByRadians:rotation]; // counterclockwise rotation
[myPath transformUsingAffineTransform: transform];
pathIsAtCenter = YES;
}
- (BOOL) containsPoint: (NSPoint) inPoint {
return [myPath containsPoint:inPoint];
}
- (float) pathArea { // this assumes that the path has not
NSPoint pathCenter = {0,0};
if (pathIsAtCenter) {
pathCenter = center;
}
// calculate the total area
float totalArea = 0;
PolarPoint polarPts[kMaxNumPolygonPoints];
short myNumPoints = 0;
NSPoint points[3];
for (short i = 0; i < [myPath elementCount] - 1; i++) { // last element is same as first, for closed path, which this is
NSBezierPathElement element = [myPath elementAtIndex: i associatedPoints: points];
if (element == NSMoveToBezierPathElement || element == NSLineToBezierPathElement) {
NSPoint offset = {points[0].x - pathCenter.x, points[0].y - pathCenter.y};
polarPts[myNumPoints].radius = sqrt(offset.x * offset.x + offset.y * offset.y);
polarPts[myNumPoints].angle = atan(offset.y / offset.x);
if (offset.x < 0)
polarPts[myNumPoints].angle += pi; // the atan(y/x) gives identical answers for (2/3) and (-2/-3),
// but the latter is 180° away from the former. This fixes that.
myNumPoints++;
}
}
PolarPoint thisPoint, nextPoint;
for (short thisPointNum = 0; thisPointNum < myNumPoints; thisPointNum++) { // for each point
thisPoint = polarPts[thisPointNum];
if (thisPointNum == myNumPoints-1) {
nextPoint = polarPts[0];
} else {
nextPoint = polarPts[thisPointNum+1];
}
float angleAfter = nextPoint.angle - thisPoint.angle;
totalArea += thisPoint.radius * nextPoint.radius * sin(angleAfter) * 0.5;
}
return totalArea;
}
#define rotation_key @"rotation"
- (void)encodeWithCoder:(NSCoder *)coder {
[super encodeWithCoder:coder];
[coder encodeFloat:rotation forKey:rotation_key];
}
- (id)initWithCoder:(NSCoder *)decoder {
self = [super initWithCoder:decoder];
rotation = [decoder decodeFloatForKey:rotation_key];
pathIsAtCenter = YES;
return self;
}
@end