The problem of calculating the intersection between a ray and a triangle is well-known. For this there exists e.g. the Möller-Trumbore intersection algorithm.
For my application I need an algorithm which efficiently computes the intersection between a polynomial curve (i.e. a "curved ray" to say it so) and a triangle. But unfortunately I was not able to find any algorithm which is adapted to this situation.
Hence, my question is: Is there an (established) algorithm, which calculates efficiently the intersection of a polynomial curve with a triangle?
A=B(Abeing equations of the triangle, andBthe equations of the polynomial). If a triangle is just 3 lines (with boundary conditions), you can compare your polynomial equation against each line to find a point such thatA1=B,A2=BorA3=B(the "roots", if you would, whereB-A#=0). A plane follows similar logic. Those are the intersections, and solving a math equation has numerous approaches, some more performant than others. Right triangles may benefit from a rotation of the curve and elimination of multiple axis.Möller-Trumboreis essentially the same "triviality" as the "ray-triangle intersection problem" you mention, using assumptions of parallelism. Polynomial curves that are continuous and differentiable everywhere would fall under similar assumptions (continuity, eventually crossing the domain area of the triangle), but the essence is the same: "do conditions exist that necessitate this math-construct will intersect our triangle". Just because they're "algorithms" doesn't mean they don't represent core mathematics questions that fit well (and end up answered) on the math SE.