如何计算一个箭头的基础上的箭头的坐标？ [英] How to calculate the coordinates of a arrowhead based on the arrow?

问题描述

我有一条线，基于两个（X，Y）坐标我知道。此线具有开始和结束点。现在，我想在该行的终点添加一个箭头。

I have a line that is based on two (x,y) coordinates I know. This line has a starting and an end point. Now I want to add an arrowhead at the end point of the line.

我知道，箭头是一个等边三角形，因此每个角度是60度。此外，我知道有一个边的长度，这将是20。我还三角形的没有一个边缘（即线的终点）。

I know that the arrow is an equilateral triangle, and therefore each angle has 60 degrees. Additionally, I know the length of one side, which will be 20. I also no one edge of the triangle (that is the end point of the line).

我如何计算其他两个点的三角形？我知道我应该用一些三角函数但如何？

How can I calculate the other two points of the triangle? I know I should use some trigonometry but how?

P.S。该生产线的终点应该是箭头的顶端。

P.s. The endpoint of the line should be the arrowhead's tip.

推荐答案

您不需要触发，只是一些向量运算...

You don't need trig., just some vector arithmetic...

说行云从A到B，用箭头的前顶点在B箭头的长度为h = 10（√3）及其半宽为w = 10，我们将表示从A单位向量为B为U =（B - A）/ | B - A | （即，差异由差分的长度划分），并垂直于该为V =单位矢量。[-U <子>是，＆NBSP; U <子> X ]

Say the line goes from A to B, with the front vertex of the arrowhead at B. The length of the arrowhead is h = 10(√3) and its half-width is w = 10. We'll denote the unit vector from A to B as U = (B - A)/|B - A| (i.e., the difference divided by the length of the difference), and the unit vector perpendicular to this as V = [-U_y, U_x].

从这些量，可以计算出箭头的两个后置的顶点为B - 胡±WV

From these quantities, you can calculate the two rear vertices of the arrowhead as B - hU ± wV.

在C ++：

struct vec { float x, y; /* … */ };

void arrowhead(vec A, vec B, vec& v1, vec& v2) {
    float h = 10*sqrtf(3), w = 10;
    vec U = (B - A)/(B - A).length();
    vec V = vec(-U.y, U.x);
    v1 = B - h*U + w*V;
    v2 = B - h*U - w*V;
}

如果你想指定不同的角度，那么你将需要一些触发。计算 ^ h 和不同的值是W 。假设你想要的长度h和尖部 - 角θ，则w = H＆NBSP一个箭头;黄褐色（θ/ 2）。然而在实践中，这是最简单的指定 ^ h 和是W 直接

If you want to specify different angles, then you will need some trig. to calculate different values of h and w. Assuming you want an arrowhead of length h and tip-angle θ, then w = h tan(θ/2). In practice, however, it's simplest to specify h and w directly.

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