我使用贝塞尔曲线的参数化表达式来定位曲线上的一个点并且它正常工作。问题是我将t值设置为y轴的百分比，不幸的是（显然）它不相关，因为我的曲线比Y轴长。所以在这个程序中，如果我将Y值设置为75，我想返回位于Y值为25的线上的点（反之因为在iOS中，（0,0）位于左上角而不是底部如我的图所示左）。目前设置我的Y值会使我的曲线上的点重新调整为75％，其Y值为15.62。
任何人都建议如何将我的曲线上的点设为Y而不是75％？
这是前一个问题finding a point on a path的后续问题，但我觉得它有足够的不同以保证其自己的主题。
#import "GraphView.h"
@interface GraphView ()
{
float yVal;
}
@end
@implementation GraphView
@synthesize myLabel, yValue;
- (id)initWithCoder:(NSCoder *)aDecoder
{
self = [super initWithCoder:aDecoder];
if (self) {
yVal = 50;
}
return self;
}
- (IBAction)yValueTextField:(id)sender
{
yVal = yValue.text.intValue;
[self resignFirstResponder];
[self setNeedsDisplay];
}
- (void)drawRect:(CGRect)rect
{
float t = yVal / 100;
// Starting point
float p1x = 0;
float p1y = 100;
// Control point 1
float c1x = 50;
float c1y = 100;
// Control point 2
float c2x = 50;
float c2y = 0;
// End Point
float p2x = 100;
float p2y = 0;
CGPoint p1 = CGPointMake(p1x, p1y);
CGPoint c1 = CGPointMake(c1x, c1y);
CGPoint c2 = CGPointMake(c2x, c2y);
CGPoint p2 = CGPointMake(p2x, p2y);
// Cubic Bezier Curver Parmetic Expression
float X = pow((1 - t), 3) * p1x + 3 * pow((1 - t), 2) * t * c1x + 3 * (1 - t) * pow(t, 2) * c2x + pow(t, 3) * p2x;
float Y = pow((1 - t), 3) * p1y + 3 * pow((1 - t), 2) * t * c1y + 3 * (1 - t) * pow(t, 2) * c2y + pow(t, 3) * p2y;
myLabel.text = [NSString stringWithFormat:@"Coord = %.2f, %.2f", X, Y];
UIBezierPath *circle = [UIBezierPath bezierPathWithOvalInRect:CGRectMake((X - 2), (Y - 2), 4, 4)];
[[UIColor blackColor] setFill];
[circle fill];
UIBezierPath *curve = [[UIBezierPath alloc] init];
[curve moveToPoint:p1];
[curve addCurveToPoint:p2 controlPoint1:c1 controlPoint2:c2];
[curve setLineWidth:1];
[[UIColor blueColor] setStroke];
[curve stroke];
}
@end
答案 0 :(得分：0)
这是我在bezier曲线上找到我的观点的解决方案。有关这方面的更多背景，请参阅我的另一篇相关文章 - ＆gt; 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