Here is my solution to finding my point on my bezier curve. For more background regarding this see another related post of mine --> finding a point on a path
#import "Calculation.h"
@implementation Calculation
@synthesize a, b, c, d, xy;
- (float) calc
{
float squareRootCalc =
sqrt(
6*pow(xy,2)*b*d
+4*a*pow(c,3)
-3*pow(b,2)*pow(c,2)
+9*pow(xy,2)*pow(c,2)
-6*a*c*b*d
+6*a*xy*c*b
-18*pow(xy,2)*b*c
+6*a*pow(xy,2)*c
-12*a*xy*pow(c,2)
-2*pow(a,2)*xy*d
+pow(a,2)*pow(d,2)
+4*pow(b,3)*d
+pow(xy,2)*pow(d,2)
-4*pow(b,3)*xy
-4*pow(c,3)*xy
+pow(a,2)*pow(xy,2)
+6*c*b*d*xy
+6*a*c*d*xy
+6*a*b*d*xy
-12*pow(b,2)*d*xy
+6*xy*c*pow(b,2)
+6*xy*b*pow(c,2)
-2*a*pow(xy,2)*d
-2*a*xy*pow(d,2)
-6*c*d*pow(xy,2)
+9*pow(xy,2)*pow(b,2)
-6*a*pow(xy,2)*b)
;
float aCalc = 24*c*d*xy + 24*a*pow(c,2) - 36*xy*pow(c,2) + 4 * squareRootCalc * a;
float bCalc = -12 * squareRootCalc * b;
float cCalc = 12 * squareRootCalc * c;
float dCalc = -4 * squareRootCalc * d;
float xyCalc =
24*xy*a*b
-24*xy*b*d
-12*b*a*d
-12*c*a*d
-12*c*b*d
+8*xy*a*d
+8*pow(b,3)
+8*pow(c,3)
+4*pow(a,2)*d
+24*pow(b,2)*d
-4*xy*pow(a,2)
-4*xy*pow(d,2)
+4*a*pow(d,2)
-12*c*pow(b,2)
-12*b*pow(c,2)
-12*a*b*c
-24*xy*a*c
+72*xy*c*b
-36*xy*pow(b,2)
;
float cubeRootCalc = cbrt(aCalc + bCalc + cCalc + dCalc + xyCalc);
float denomCalc = (a-3*b+3*c-d);
float secOneCalc = 0.5 * cubeRootCalc / denomCalc;
float secTwoCalc = -2 * ((a*c - a*d - pow(b,2) + c*b + b*d - pow(c,2)) / (denomCalc * cubeRootCalc));
float secThreeCalc = (a - 2*b + c) / denomCalc;
return secOneCalc + secTwoCalc + secThreeCalc;
}
- (Calculation *) initWithA:(float)p0 andB:(float)p1 andC:(float)p2 andD:(float)p3 andXy:(float)xyValue
{
self = [super init];
if (self) {
[self setA:p0];
[self setB:p1];
[self setC:p2];
[self setD:p3];
[self setXy:xyValue];
}
return self;
}
- (void) setA:(float)p0 andB:(float)p1 andC:(float)p2 andD:(float)p3 andXy:(float)xyValue
{
[self setA:p0];
[self setB:p1];
[self setC:p2];
[self setD:p3];
[self setXy:xyValue];
}
@end