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-//
-// util.m
-// TikZiT
-//
-// Copyright 2010 Aleks Kissinger. All rights reserved.
-//
-//
-// This file is part of TikZiT.
-//
-// TikZiT is free software: you can redistribute it and/or modify
-// it under the terms of the GNU General Public License as published by
-// the Free Software Foundation, either version 3 of the License, or
-// (at your option) any later version.
-//
-// TikZiT is distributed in the hope that it will be useful,
-// but WITHOUT ANY WARRANTY; without even the implied warranty of
-// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-// GNU General Public License for more details.
-//
-
-#import "util.h"
-#import "math.h"
-
-static BOOL fuzzyCompare(float f1, float f2) {
- return (ABS(f1 - f2) <= 0.00001f * MIN(ABS(f1), ABS(f2)));
-}
-
-NSRect NSRectWithPoint(NSRect rect, NSPoint p) {
- CGFloat minX = NSMinX(rect);
- CGFloat maxX = NSMaxX(rect);
- CGFloat minY = NSMinY(rect);
- CGFloat maxY = NSMaxY(rect);
- if (p.x < minX) {
- minX = p.x;
- } else if (p.x > maxX) {
- maxX = p.x;
- }
- if (p.y < minY) {
- minY = p.y;
- } else if (p.y > maxY) {
- maxY = p.y;
- }
- return NSMakeRect(minX, minY, maxX - minX, maxY - minY);
-}
-
-NSRect NSRectAroundPointsWithPadding(NSPoint p1, NSPoint p2, float padding) {
- return NSMakeRect(MIN(p1.x,p2.x)-padding,
- MIN(p1.y,p2.y)-padding,
- ABS(p2.x-p1.x)+(2.0f*padding),
- ABS(p2.y-p1.y)+(2.0f*padding));
-}
-
-NSRect NSRectAroundPoints(NSPoint p1, NSPoint p2) {
- return NSRectAroundPointsWithPadding(p1, p2, 0.0f);
-}
-
-NSRect NSRectAround4PointsWithPadding(NSPoint p1, NSPoint p2, NSPoint p3, NSPoint p4, float padding) {
- float leftMost = MIN(p1.x, p2.x);
- leftMost = MIN(leftMost, p3.x);
- leftMost = MIN(leftMost, p4.x);
- float rightMost = MAX(p1.x, p2.x);
- rightMost = MAX(rightMost, p3.x);
- rightMost = MAX(rightMost, p4.x);
- float topMost = MIN(p1.y, p2.y);
- topMost = MIN(topMost, p3.y);
- topMost = MIN(topMost, p4.y);
- float bottomMost = MAX(p1.y, p2.y);
- bottomMost = MAX(bottomMost, p3.y);
- bottomMost = MAX(bottomMost, p4.y);
- return NSMakeRect(leftMost-padding,
- topMost-padding,
- (rightMost - leftMost)+(2.0f*padding),
- (bottomMost - topMost)+(2.0f*padding));
-}
-
-NSRect NSRectAround4Points(NSPoint p1, NSPoint p2, NSPoint p3, NSPoint p4) {
- return NSRectAround4PointsWithPadding(p1, p2, p3, p4, 0.0f);
-}
-
-float NSDistanceBetweenPoints(NSPoint p1, NSPoint p2) {
- float dx = p2.x - p1.x;
- float dy = p2.y - p1.y;
- return sqrt(dx * dx + dy * dy);
-}
-
-float good_atan(float dx, float dy) {
- if (dx > 0) {
- return atan(dy/dx);
- } else if (dx < 0) {
- return M_PI + atan(dy/dx);
- } else {
- if (dy > 0) return 0.5 * M_PI;
- else if (dy < 0) return 1.5 * M_PI;
- else return 0;
- }
-}
-
-// interpolate on a cubic bezier curve
-float bezierInterpolate(float dist, float c0, float c1, float c2, float c3) {
- float distp = 1 - dist;
- return (distp*distp*distp) * c0 +
- 3 * (distp*distp) * dist * c1 +
- 3 * (dist*dist) * distp * c2 +
- (dist*dist*dist) * c3;
-}
-
-NSPoint bezierInterpolateFull (float dist, NSPoint c0, NSPoint c1, NSPoint c2, NSPoint c3) {
- return NSMakePoint (bezierInterpolate (dist, c0.x, c1.x, c2.x, c3.x),
- bezierInterpolate (dist, c0.y, c1.y, c2.y, c3.y));
-}
-
-static void lineCoeffsFromPoints(NSPoint p1, NSPoint p2, float *A, float *B, float *C) {
- *A = p2.y - p1.y;
- *B = p1.x - p2.x;
- *C = (*A) * p1.x + (*B) * p1.y;
-}
-
-static void lineCoeffsFromPointAndAngle(NSPoint p, float angle, float *A, float *B, float *C) {
- *A = sin (angle);
- *B = -cos (angle);
- *C = (*A) * p.x + (*B) * p.y;
-}
-
-static BOOL lineSegmentContainsPoint(NSPoint l1, NSPoint l2, float x, float y) {
- float minX = MIN(l1.x, l2.x);
- float maxX = MAX(l1.x, l2.x);
- float minY = MIN(l1.y, l2.y);
- float maxY = MAX(l1.y, l2.y);
- return (x >= minX || fuzzyCompare (x, minX)) &&
- (x <= maxX || fuzzyCompare (x, maxX)) &&
- (y >= minY || fuzzyCompare (y, minY)) &&
- (y <= maxY || fuzzyCompare (y, maxY));
-}
-
-BOOL lineSegmentsIntersect(NSPoint l1start, NSPoint l1end, NSPoint l2start, NSPoint l2end, NSPoint *result) {
- // Ax + By = C
- float A1, B1, C1;
- lineCoeffsFromPoints(l1start, l1end, &A1, &B1, &C1);
- float A2, B2, C2;
- lineCoeffsFromPoints(l2start, l2end, &A2, &B2, &C2);
-
- float det = A1*B2 - A2*B1;
- if (det == 0.0f) {
- // parallel
- return NO;
- } else {
- float x = (B2*C1 - B1*C2)/det;
- float y = (A1*C2 - A2*C1)/det;
-
- if (lineSegmentContainsPoint(l1start, l1end, x, y) &&
- lineSegmentContainsPoint(l2start, l2end, x, y)) {
- if (result) {
- (*result).x = x;
- (*result).y = y;
- }
- return YES;
- }
- }
- return NO;
-}
-
-BOOL lineSegmentIntersectsBezier (NSPoint lstart, NSPoint lend, NSPoint c0, NSPoint c1, NSPoint c2, NSPoint c3, NSPoint *result) {
- NSRect curveBounds = NSRectAround4Points(c0, c1, c2, c3);
- if (!lineSegmentIntersectsRect(lstart, lend, curveBounds))
- return NO;
-
- const int divisions = 20;
- const float chunkSize = 1.0f/(float)divisions;
- float chunkStart = 0.0f;
- BOOL found = NO;
-
- for (int i = 0; i < divisions; ++i) {
- float chunkEnd = chunkStart + chunkSize;
-
- NSPoint p1 = bezierInterpolateFull (chunkStart, c0, c1, c2, c3);
- NSPoint p2 = bezierInterpolateFull (chunkEnd, c0, c1, c2, c3);
-
- NSPoint p;
- if (lineSegmentsIntersect (lstart, lend, p1, p2, &p)) {
- lstart = p;
- found = YES;
- }
-
- chunkStart = chunkEnd;
- }
- if (found && result) {
- *result = lstart;
- }
- return found;
-}
-
-BOOL lineSegmentIntersectsRect(NSPoint lineStart, NSPoint lineEnd, NSRect rect) {
- const float rectMaxX = NSMaxX(rect);
- const float rectMinX = NSMinX(rect);
- const float rectMaxY = NSMaxY(rect);
- const float rectMinY = NSMinY(rect);
-
- // check if the segment is entirely to one side of the rect
- if (lineStart.x > rectMaxX && lineEnd.x > rectMaxX) {
- return NO;
- }
- if (lineStart.x < rectMinX && lineEnd.x < rectMinX) {
- return NO;
- }
- if (lineStart.y > rectMaxY && lineEnd.y > rectMaxY) {
- return NO;
- }
- if (lineStart.y < rectMinY && lineEnd.y < rectMinY) {
- return NO;
- }
-
- // Now check whether the (infinite) line intersects the rect
- // (if it does, so does the segment, due to above checks)
-
- // Ax + By = C
- float A, B, C;
- lineCoeffsFromPoints(lineStart, lineEnd, &A, &B, &C);
-
- const float tlVal = A * rectMinX + B * rectMaxY - C;
- const float trVal = A * rectMaxX + B * rectMaxY - C;
- const float blVal = A * rectMinX + B * rectMinY - C;
- const float brVal = A * rectMaxX + B * rectMinY - C;
-
- if (tlVal < 0 && trVal < 0 && blVal < 0 && brVal < 0) {
- // rect below line
- return NO;
- }
- if (tlVal > 0 && trVal > 0 && blVal > 0 && brVal > 0) {
- // rect above line
- return NO;
- }
-
- return YES;
-}
-
-NSPoint findExitPointOfRay (NSPoint p, float angle_rads, NSRect rect) {
- const float rectMinX = NSMinX (rect);
- const float rectMaxX = NSMaxX (rect);
- const float rectMinY = NSMinY (rect);
- const float rectMaxY = NSMaxY (rect);
-
- const float angle = normaliseAngleRad (angle_rads);
-
- // special case the edges
- if (p.y == rectMaxY && angle > 0 && angle < M_PI) {
- // along the top of the box
- return p;
- }
- if (p.y == rectMinY && angle < 0 && angle > -M_PI) {
- // along the bottom of the box
- return p;
- }
- if (p.x == rectMaxX && angle > -M_PI/2.0f && angle < M_PI/2.0f) {
- // along the right of the box
- return p;
- }
- if (p.x == rectMinX && (angle > M_PI/2.0f || angle < -M_PI/2.0f)) {
- // along the left of the box
- return p;
- }
-
- float A1, B1, C1;
- lineCoeffsFromPointAndAngle(p, angle, &A1, &B1, &C1);
- //NSLog(@"Ray is %fx + %fy = %f", A1, B1, C1);
-
- const float tlAngle = normaliseAngleRad (good_atan (rectMinX - p.x, rectMaxY - p.y));
- const float trAngle = normaliseAngleRad (good_atan (rectMaxX - p.x, rectMaxY - p.y));
- if (angle <= tlAngle && angle >= trAngle) {
- // exit top
- float A2, B2, C2;
- lineCoeffsFromPoints(NSMakePoint (rectMinX, rectMaxY),
- NSMakePoint (rectMaxX, rectMaxY),
- &A2, &B2, &C2);
- float det = A1*B2 - A2*B1;
- NSCAssert(det != 0.0f, @"Parallel lines?");
- NSPoint intersect = NSMakePoint ((B2*C1 - B1*C2)/det,
- (A1*C2 - A2*C1)/det);
- return intersect;
- }
-
- const float brAngle = normaliseAngleRad (good_atan (rectMaxX - p.x, rectMinY - p.y));
- if (angle <= trAngle && angle >= brAngle) {
- // exit right
- float A2, B2, C2;
- lineCoeffsFromPoints(NSMakePoint (rectMaxX, rectMaxY),
- NSMakePoint (rectMaxX, rectMinY),
- &A2, &B2, &C2);
- //NSLog(@"Edge is %fx + %fy = %f", A2, B2, C2);
- float det = A1*B2 - A2*B1;
- NSCAssert(det != 0.0f, @"Parallel lines?");
- NSPoint intersect = NSMakePoint ((B2*C1 - B1*C2)/det,
- (A1*C2 - A2*C1)/det);
- return intersect;
- }
-
- const float blAngle = normaliseAngleRad (good_atan (rectMinX - p.x, rectMinY - p.y));
- if (angle <= brAngle && angle >= blAngle) {
- // exit bottom
- float A2, B2, C2;
- lineCoeffsFromPoints(NSMakePoint (rectMaxX, rectMinY),
- NSMakePoint (rectMinX, rectMinY),
- &A2, &B2, &C2);
- float det = A1*B2 - A2*B1;
- NSCAssert(det != 0.0f, @"Parallel lines?");
- NSPoint intersect = NSMakePoint ((B2*C1 - B1*C2)/det,
- (A1*C2 - A2*C1)/det);
- return intersect;
- } else {
- // exit left
- float A2, B2, C2;
- lineCoeffsFromPoints(NSMakePoint (rectMinX, rectMaxY),
- NSMakePoint (rectMinX, rectMinY),
- &A2, &B2, &C2);
- float det = A1*B2 - A2*B1;
- NSCAssert(det != 0.0f, @"Parallel lines?");
- NSPoint intersect = NSMakePoint ((B2*C1 - B1*C2)/det,
- (A1*C2 - A2*C1)/det);
- return intersect;
- }
-}
-
-float roundToNearest(float stepSize, float val) {
- if (stepSize==0.0f) return val;
- else return round(val/stepSize)*stepSize;
-}
-
-float radiansToDegrees (float radians) {
- return (radians * 180.0f) / M_PI;
-}
-
-float degreesToRadians(float degrees) {
- return (degrees * M_PI) / 180.0f;
-}
-
-int normaliseAngleDeg (int degrees) {
- while (degrees > 180) {
- degrees -= 360;
- }
- while (degrees <= -180) {
- degrees += 360;
- }
- return degrees;
-}
-
-float normaliseAngleRad (float rads) {
- while (rads > M_PI) {
- rads -= 2 * M_PI;
- }
- while (rads <= -M_PI) {
- rads += 2 * M_PI;
- }
- return rads;
-}
-
-static char ahex[] =
-{'a','b','c','d','e','f','g','h','i','j',
- 'A','B','C','D','E','F'};
-
-NSString *alphaHex(unsigned short sh) {
- if (sh > 255) return @"!!";
- return [NSString stringWithFormat:@"%c%c", ahex[sh/16], ahex[sh%16]];
-}
-
-const char *find_start_of_nth_line (const char * string, int line) {
- int l = 0;
- const char *lineStart = string;
- while (*lineStart && l < line) {
- while (*lineStart && *lineStart != '\n') {
- ++lineStart;
- }
- if (*lineStart) {
- ++l;
- ++lineStart;
- }
- }
- return lineStart;
-}
-
-
-// vi:ft=objc:noet:ts=4:sts=4:sw=4
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