如何在3D空间中检测点是否在圆锥内部？ [英] How can I detect if a point is inside a cone or not, in 3D space?

问题描述

如何检测3D点是否在锥体内？

  Ross cone =（x1，y1，h1）
锥角= alpha 
锥高= H 
锥形半径= R 
锥形点的坐标= P1（x2，y2，h2）
锥形外的坐标= P2（x3，y3，h3）
 
 point1 = true的结果
 point2的结果= false 
  

方案

要扩展Ignacio的答案：

让

  x =锥体的尖端
 dir =归一化轴向量，从尖端指向基础
h = height 
r =基本半径
 
p =指向测试
  

所以你的项目 p 到 dir 以找到点沿着轴的距离：

  cone_dist =点（p-x，dir）
  

此时，您可以拒绝<$ c $然后你计算沿着该点的那个点的圆锥半径：

  cone_radius =（cone_dist / h）* r 
  

最后计算点与轴相对锥体半径的正交距离：

  orth_distance = length（（p-x）-conce_dist * dir）
 
 is_point_inside_cone =（orth_distance< cone_radius）
  

How is possible to detect if a 3D point is inside a cone or not?

Ross cone = (x1, y1, h1)
Cone angle = alpha
Height of the cone = H
Cone radius = R
Coordinates of the point of the cone = P1 (x2, y2, h2)
Coordinates outside the cone = P2( x3, y3, h3)

Result for point1 = true
Result for point2 = false

解决方案

To expand on Ignacio's answer:

Let

x = the tip of the cone
dir = the normalized axis vector, pointing from the tip to the base
h = height
r = base radius

p = point to test

So you project p onto dir to find the point's distance along the axis:

cone_dist = dot(p - x, dir)

At this point, you can reject values outside 0 <= cone_dist <= h.

Then you calculate the cone radius at that point along the axis:

cone_radius = (cone_dist / h) * r

And finally calculate the point's orthogonal distance from the axis to compare against the cone radius:

orth_distance = length((p - x) - cone_dist * dir)

is_point_inside_cone = (orth_distance < cone_radius)

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