三角形中的矩形

Question

I am trying to build a program in C++ that will procedurally generate cities. For the moment, the city is represented by an array of blocks either Quad blocks or Triangle blocks.

I can't find an effective way to subdivide a triangle (TBlock) into a rectangle (QBlock) and three triangles.

So picture a triangle ABC. We have two point T and T' which are the first and second tier of line segment BC. Now I need to find P and P' which are respectively on AB and AC line segments. P is the intersection of AB and the normal of BC passing through T. P' is the intersection of AB and the normal of BC passing through T'.

I know how to find T and T' and the inward normal of vector BC but I can't find a way to compute the normal passing through T or T'.

Thanks !

Answer 1

Given your (BC) vector is (x, y), a normal vector of BC is (-y, x). Now offset the normal vector by coordinates of T', and you will get the normal of BC passing through T'.

Answer 2

the normal to a line y = m*x + c is the line y = (-1/m)*x + d , where c and d are constants. You have two lines with a common point (T or T'), you can solve simultaneously to find m and d for both T and T'.

Answer 3

You know that the angle formed by CBA is the same angle formed by TBP. Let's call that O. You also know the distance between B and T. Call it D. Using this we can find P using trigonometry.

Tan(O) = X / D

Where X is the y_axis distance between T and P. Just solve for X since you know O and D.

Once you know X you can just add X to the y value of T to find P.