Barycentric Coordinates for Point-in-Triangle Tests

Write a C program that computes barycentric coordinates and tests whether points are inside a triangle.

Requirements:

• Define a triangle with vertices A=(2,2), B=(8,3), C=(5,8)
• Implement an edge function: edge(P, A, B) = (B.x - A.x)(P.y - A.y) - (B.y - A.y)(P.x - A.x)
• Compute the triangle's signed area: area = edge(A, B, C)
• For each of these test points: (5, 4), (10, 10), (2, 2), (5, 8), (8, 3):
  • Compute barycentric coordinates (u, v, w)
  • Determine if the point is inside, on an edge, or outside
  • Print the coordinates and the classification
• Also test a grid of points from x=0..10 and y=0..10, counting how many are inside
• Print the total count of interior grid points
• Show the formula used for edge function and barycentric coordinates