Create shape from points / lines in editor and mathematically calculate nearest points within shape

Question

If I want an editor that accepts "points" of a minimum of three (a triangle) and I just add some points first, like this:

how can I mathematically connect these corners (points) into an object of multiple triangles? so amount of triangles looks like something like this, by connecting nearest point:

and then later render this and also being able to define what it is and check for collisions on this ground, so I can create more than Rectangle based "bricks" on a Platformer for example. Also being able to texturize the whole object without it looking ugly.

Any ideas? Or what is this called in game programming?

Answer 1

What you are describing looks to me like a triangle strip. Riemer has a tutorial for creating these in an efficient manner. So if user adds a point you just add one along the bottom of the shape and then create the triangles using the points in a clockwise manner, but the tutorial covers this quite well.

EDIT: For collision detection between points you can linearly interpolate between them and check the height value of your object and the interpolated points.