Slope, intercept, distance, etc., between points.

MADMathAlgebra.h

//
//  MADMathAlgebra.h
//  MADCocoaExtensions
//
//  Created by Michael Thomason on 5/23/16.
//  Copyright © 2017 Michael Thomason. All rights reserved.
//

#ifndef MADMathAlgebra_h
#define MADMathAlgebra_h

#import "MADLineSegment.h"

static inline double CGAngleBetweenTwoPoints(CGPoint p1, CGPoint p2);
static inline double CGAngleBetweenTwoPoints(CGPoint p1, CGPoint p2) {
	return atan2(p2.y - p1.y, p2.x - p1.x) * (180.0000 / M_PI);
}

static inline double MADDistance(CGPoint p1, CGPoint p2);
static inline double MADDistance(CGPoint p1, CGPoint p2) {
	return sqrt(pow((p2.x - p1.x), 2) + pow((p2.y - p1.y), 2));
}

static inline CGFloat CGSlope(CGPoint p1, CGPoint p2);
static inline CGFloat CGSlope(CGPoint p1, CGPoint p2) {
	CGFloat d = (p2.x - p1.x);
	return d > FLT_EPSILON ? ((p2.y - p1.y) / d) : 0.0000f;
}

static inline CGFloat CGIntercept(CGFloat y, CGPoint p1, CGPoint p2);
static inline CGFloat CGIntercept(CGFloat y, CGPoint p1, CGPoint p2) {
	//y = m x + b;
	CGFloat m = ((p2.y - p1.y) / (p2.x - p1.x));
	CGFloat b = p1.y - (m * p1.x);
	return (y - b) / m;
}

static inline CGFloat MADLineSegmentSlope(MADLineSegment lineSegment);
static inline CGFloat MADLineSegmentSlope(MADLineSegment lineSegment) {
	return CGSlope(lineSegment.start, lineSegment.end);
}

static inline double CGInterceptBySlope(CGPoint p2, double m);
static inline double CGInterceptBySlope(CGPoint p2, double m) {
	return (p2.y - (m * p2.x));
}

static inline CGPoint CGYInversePlusDistance(CGPoint p1, CGPoint p2, CGFloat d);
static inline CGPoint CGYInversePlusDistance(CGPoint p1, CGPoint p2, CGFloat d) {
	CGPoint returnVal = CGPointZero;
	double m = -1 * MADDistance(p1, p2);
	double b = CGInterceptBySlope(p2, m);
	double x = p2.x;
	double y = p2.y;
	BOOL movingUp = p1.y < p2.y;
	
	if (d >= 0) {
		double mPow2 = pow(m, 2);
		double bPow2 = pow(b, 2);
		double dPow2 = pow(d, 2);
		double u = p2.x;
		double v = p2.y;
		double sqrtPart = 0.0;
		sqrtPart = (mPow2)*( ((-1)*(bPow2)) + ((dPow2)*(1+mPow2)) -
							(pow((((-1)*(m)*(u)) + v),2)) + (b*(((-1)*(2)*(m)*(u))+((2)*(v)))) );
		if (!isnan(sqrtPart)) {
			if (movingUp) y = ((b)+((m)*(u))+((mPow2)*(v))+sqrt(sqrtPart)) / (1+mPow2);
			else y = ((b)+((m)*(u))+((mPow2)*(v))-sqrt(sqrtPart)) / (1+mPow2);
			
			x=(y-b)/m;
		}
		if (!isnan(x) && !isnan(y)) {
			returnVal.x = (CGFloat)x;
			returnVal.y = (CGFloat)y;
		} else {
			returnVal.x = p2.x;
			returnVal.y = p2.y;
		}
	}
	return returnVal;
}

#endif /* MADMathAlgebra_h */