Given there is triangle: V in 3D space that transforms over time t -> t1 to V1, and a static point P is somewhere in 3d space, how can I determine if P ever collides with V, and if so at what value of t?


The transformation of the triangle from V -> V1 over time means the vertices Va,Vb,Vc each move linearly and independently in three dimensions to new vertex positions V1a,V1b,V1c. (Sorry about my notation). There are no constraints on the transformation of the vertices with respect to each other. The triangles at V and V1 representing the transformation may be any 2 triangles in 3d space.



find the collision of a particle with a swept triangle.
This type of problem is usually called "continuous collision detection". There is a substantial literature on this subject as you'll discover if you try a [google search](http://www.google.com/search?q=%22continuous+collision+detection%22) on those key words. It's rare that someone wants to do this for one triangle at a time. The literature has techniques for checking against large sets of triangles as well as generalisations to alternative shapes and more complex motion such as quadratic motion wrt time.


