这个算法的需求是需要把已知的一系列坐标有序连接起来的折线按间距等分。
用到的数学知识点是 ：
定比分点
定比分点-摘自百度百科
示例图
图中黄点是已知的有序坐标，绿线是由黄点连接起来的折线，红点就是所求的等分点了。
此算法是我朋友写的，我把它写成了OC版然后帮助测试了一下。
声明部分：
@property (nonatomic, assign) CGFloat spacing; // 间距
@property (nonatomic, assign) CGFloat distanceSum; // 总距离的和
@property (nonatomic, assign) CGFloat surplusDistance; //上一段线段剩余的距离
@property (nonatomic, strong) NSArray *pointArr; // 折线点数组
@property (nonatomic, strong) NSMutableArray *spacingPoints; // 存放等分点的数组
@property (nonatomic, strong) NSMutableArray *distanceArr; // 存放折线中每两点间距的数组
辅助方法：
/**
* 计算总长度
*/
- (NSMutableArray *)calculateDistanceSum:(NSArray *)points
{
// 存放两点间间距的数组
NSMutableArray *pointDistance = [NSMutableArray array];
for (int i = 0; i < points.count - 1; i++) {
CGPoint point1 = [points[i] CGPointValue];
CGPoint point2 = [points[i+1] CGPointValue];
self.distanceSum += [self calculateDistance:point1 :point2];
[pointDistance addObject:[NSNumber numberWithDouble:[self calculateDistance:point1 :point2]]];
}
return pointDistance;
}
/**
* 计算两点的间距
*
* @param point1 点A
* @param point2 点B
* @return 间距
*/
- (double)calculateDistance:(CGPoint)point1 :(CGPoint)point2
{
double x = pow(point1.x - point2.x, 2);
double y = pow(point1.y - point2.y, 2);
double result = sqrt(x + y);
return result;
}
/**
* 计算λ
*
* @param s 折线上两点间的间距
* @param n spacing - surplusDistance;
* @return λ
*/
- (double)calculateLambda:(double)s :(double)n
{
double lambda = n / (s - n);
return lambda;
}
/**
* 已知λ,x1,x2，计算目标坐标点x
*
* @param lambda λ
* @param x1 point1 的x
* @param x2 point2 的x
* @return 目标点x值
*/
- (double)calculateX:(double)lambda :(double)x1 :(double)x2
{
double x = (x1 + lambda * x2) / (1 + lambda);
return x;
}
/**
* 已知λ,y1,y2，计算目标坐标点y
*
* @param lambda λ
* @param y1 point1 的y
* @param y2 point2 的y
* @return 目标点y值
*/
- (double)calculateY:(double)lambda :(double)y1 :(double)y2
{
double y = (y1 + lambda * y2) / (1 + lambda);
return y;
}
主要方法：
// 开始计算
// 递归，i初始值为0
// 表示折线中的第i条线段
- (void)doCalculate:(int)i
{
CGPoint startPoint = CGPointZero;
CGPoint endPoint = CGPointZero;
if (i < self.pointArr.count - 1) {
startPoint = [self.pointArr[i] CGPointValue];
endPoint = [self.pointArr[i+1] CGPointValue];
// 存在的点个数
int pointNum = (int)(([self.distanceArr[i] doubleValue] + _surplusDistance) / self.spacing);
if (pointNum > 0) {
for (int j = 0; j < pointNum; j++) {
double n = 0;
double s = 0;
if (j == 0) {
n = self.spacing - _surplusDistance;
s = [self.distanceArr[i] doubleValue];
} else {
n = (j + 1) * self.spacing - _surplusDistance;
s = [self.distanceArr[i] doubleValue];
}
if (n != s) {
double lambda = [self calculateLambda:s :n];
double x = [self calculateX:lambda :startPoint.x :endPoint.x];
double y = [self calculateY:lambda :startPoint.y :endPoint.y];
CGPoint newPoint = CGPointMake(x, y);
[self.spacingPoints addObject:[NSValue valueWithCGPoint:newPoint]];
} else {
[self.spacingPoints addObject:[NSValue valueWithCGPoint:endPoint]];
}
}
// 更新剩余距离
_surplusDistance += [self.distanceArr[i] doubleValue] - pointNum * self.spacing;
} else {
// 更新剩余距离
_surplusDistance += [self.distanceArr[i] doubleValue] - pointNum * self.spacing;
}
[self doCalculate:i + 1];
}
}
供有需要的朋友参考。
