c++,math,3d , Detect if vertex is inside a list of points (cube)

## Question:

Tag: c++,math,3d

I want to find if a vertex is inside of a cube in a C++ program.

Take this example, I want to find all vertices of the torus that lie inside of the cube.

How would I go on doing this, knowing that my cube is just a list of points to start with (I'm parsing an .obj file)

For example, my cube vertices:

v  -56.269790649414 -100.226547241211 -29.616094589233
v  3.730209350586 -100.226547241211 -29.616094589233
v  -56.269790649414 -40.226547241211 -29.616094589233
v  3.730209350586 -40.226547241211 -29.616094589233
v  -56.269790649414 -100.226547241211 30.383905410767
v  3.730209350586 -100.226547241211 30.383905410767
v  -56.269790649414 -40.226547241211 30.383905410767
v  3.730209350586 -40.226547241211 30.383905410767

What are the best practices/algorithms to achieve this (raycasting?)

Apparently your cube is axis-parallel, so it is sufficient to check whether the vertex to test lies in the intersection of the slice of the parellel side planes. To put it differently, an axis-parallel cube is its own bounding box. Let

x_max = maximum x-coordinate of the cube
x_min = minimum x-coordinate of the cube
y_max = maximum y-coordinate of the cube
y_min = minimum y-coordinate of the cube
z_max = maximum z-coordinate of the cube
Z_min = minimum z-coordinate of the cube

then a point (x,y,z) is contained in the cube if and only if

x_min <= x <= x_max && y_min <= y <= y_max && z_min <= z <= Z_max

However things are more complicated if the cube is actually not axis-parallel.

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