通过中心，法线，长度和高度获取矩形顶点

Question

I am looking for a way to get all the vertices of a rectangle whose center, normal, length and height I know. I am a little weak in maths so please help me. Edit : the plane is in 3D space.

Answer 1

You can easily calculate the x and y coordinates of the vertices of a rectangle in 2D space given the center, width and height by subtracting/adding half the width/height from the x/y position of the center point.

If you need this in 3D space, this becomes a little more tricky and relies on a bit of trigonometry, but still follows the same principle. You'll need one extra piece of information. You need some way of fixing the orientation of the square in some direction; ie, which direction is the rectangle 'facing'. The normal will allow you to work out what plane the rectangle is on, but without some orientation on that plane, the best you can do is work out a set of possible values in a circle around the center for each of the vertices.