Besides the three line test, I think we might use the idea of convex hull to decide if a point exists inside the triangle.Assuming we know one vertex v0 and two vectors (V1,V2) from v0 to the other two vertices. The point v we want to test can be written as the combination of v0, aV1, bV2, where a and b can be calculated by vector determinants. Some formulas can be found here link.
Here's a desmos demo of the 3 line test.
Besides the three line test, I think we might use the idea of convex hull to decide if a point exists inside the triangle.Assuming we know one vertex v0 and two vectors (V1,V2) from v0 to the other two vertices. The point v we want to test can be written as the combination of v0, aV1, bV2, where a and b can be calculated by vector determinants. Some formulas can be found here link.