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

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

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.