This mesh has 4 vertices and 4 faces.
This mesh has 8 vertices and 12 faces.
I linearly interpolated the color from blue [0,0,1] to red [1,0,0] from the front to the back
R_relative should be rotating by -90 degrees about the z-axis and T_relative should be zero
R_relative here should be the identity and not rotating. T_relative here moves 3.5 in z
R_relative here is the identity and does not do any rotation. T_relative here is 0.5 in x and -0.5 in y
R_relative here is a rotation 90 degrees about the y axis and T_relative is -3 in x and +3 in z
Rendering a mesh is easier in terms of memory usage and speed, but a pointcloud results in a much smoother representation due to the usage of many points, but is much more memory hungry
This result was based on and adapted from the pytorch3d tutorial from here. In this, I deform the cow mesh (in red) that we were given in this assignment to a dolphin mesh (in blue). To do this, the chamfer distance is iteratively optimized for between the deformed cow geometry and the target dolphin geometry. To enforce smoothness, additional shape regularizer losses are used to minimize the length of edges in the deformed mesh, normal consistences around neighboring faces and enforce laplacian smoothing. The Stochastic gradient descent algorithm is used for the optimization. The end result is pretty close to the target dolphin mesh, with notably the cow ears not having closely converged to the dolphin shape.
