Differentiable Renderer Forward

Implement forward pass of a simple differentiable renderer to generate a 2D silhouette from a 3D mesh. This process involves projective transformations and rasterization to create an image that is differentiable with respect to the mesh vertices.

The concept of differentiable rendering is crucial in neural rendering as it allows for the optimization of 3D models using backpropagation. The rendering process can be broken down into steps:

1. Projecting 3D vertices to 2D using a projection matrix
2. Rasterizing triangles with soft boundaries to create a continuous and differentiable output
3. Ensuring the output is differentiable with respect to the vertices, enabling the computation of gradients

This technique is widely used in computer vision and graphics applications.