VEC 1 =圆心，VEC2 = mousePos结构，找到VEC 1，VEC 2之间的圆点 [英] Vec1 = Circle centre, Vec2 = mousepos, find the point on the circle between Vec1, Vec2

问题描述

我有两个矢量：一个是在一个圆的中心，另一个是在鼠标位置。我想找到的圆是两个向量之间的角度。

我特别想在圆心+直径，而不是三角学方面的答案。所以，圆心+圆直径（以方向）鼠标位置。

如果有帮助，认为一个时钟。我需要数的手所指向​​的矢量coordinance。手总是向着变量向量'鼠标的位置指点。

我要'点'（vec2d_X）的上（vec2d_1）在时钟的中心之间的圆圈的和'鼠标的位置（vec2d_2）。

也看到这个跟进的问题：
<一href="http://stackoverflow.com/questions/25925163/determine-rotation-direction-toward-variable-point-on-a-circle">Determine旋转方向/朝一个圆 /可变点

编辑>>>>>>

时使用trig的更快？

  #Python
高清circlepoint_trig（顶点，mousePos结构，circlepoint）：
    角= math.atan2（mousePos结构[1]  - 顶点[1]，mousePos结构[0]  - 顶点[0]）
    MYX = 80 * math.cos（角）＃80是时钟'手'的长度
    MYY = 80 * math.sin（角）＃80是时钟'手'的长度
    circlepoint = vec2d（MYX，MYY）+顶点
    回报circlepoint
 

解决方案

radius_vector = mouse_position - circle_center

normalized_vector = radius_vector * circle_radius / radius_vector.length（）

circle_point = circle_center + normalized_vector

澄清：

vector.length =开方（vector.x * vector.x + vector.y * vector.y）

I have two vectors: one is in the centre of a circle, another is at the mouse position. I want to find the point on the circle that is between the two vectors.

I specifically want the answer in terms of circle centre + diameter, not trigonometry. So, Circle centre + circle diameter (in the direction of) the mouse position.

If it helps, think of a clock. I need the vector coordinance of the 'number' the 'hand' is pointing to. The hand is always pointing toward the variable vector 'mouse position'.

I want 'the point'(vec2d_X) on the circle between the 'centre of the clock' (vec2d_1) and the 'mouse position'(vec2d_2).

See also this follow up question:
Determine rotation direction /toward/ variable point on a circle

EDIT>>>>>>

Is using trig faster?

#Python
def circlepoint_trig(vertex, mousepos, circlepoint):
    angle = math.atan2(mousepos[1] - vertex[1], mousepos[0] - vertex[0])
    myx = 80 * math.cos(angle) #80 is length of clock 'hand'
    myy = 80 * math.sin(angle) #80 is length of clock 'hand'
    circlepoint = vec2d(myx,myy) + vertex
    return circlepoint

解决方案

radius_vector = mouse_position - circle_center

normalized_vector = radius_vector * circle_radius / radius_vector.length()

circle_point = circle_center + normalized_vector

Clarification:

vector.length=sqrt(vector.x*vector.x+vector.y*vector.y)

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