This gif is demonstrating a 360 degree view of the cow. This is done by changing the azimuth which allows the image to rotat around the y axis
This gif is demonstrating dolly zoom. It uses the following equation in python distance = 5/(2*np.tan(0.5*np.deg2rad(fov))) T = [[0, 0, distance]]. We want to vary the distance to the camera by the width of the image. The FOV represents the field of view which is used to calculate the distance. We are translating in the z direction.
The gif below demonstrated a tetrahedron. This has 4 faces and 4 vertices.
The vertices I chose are [[0.0,0.0,0.0], [0.0,0.0,1.0], [0.0,1.0,0.0], [1.0,0.0,0.0]]
and the faces are [[0,1,2], [1,2,3], [0,1,3], [0,2,3]].
Note: I changed the elevation slightly for this one to make it evident it is a tetrahedron, or else it looked more like a triangle.
This gif is demonstrating a cube. This is made up of 2 triangular meshes per face. Since there are 6 surfaces in a cube, we need 12 faces. The number of vertices stays same at 8.
These are the vertices I chose [[0.0,0.0,0.0], [0.0,0.0,1.0], [0.0,1.0,0.0], [0.0, 1.0, 1.0], [1.0,0.0,0.0], [1.0,0.0,1.0], [1.0, 1.0, 0.0], [1.0, 1.0, 1.0]]
and the order of the faces [[0,1,2], [1,2,3], [0,2,4], [2,4,6], [1,4,5], [0,1,4], [1,3,5], [3,5,7], [5,4,6], [2,3,6], [7,3,6], [5,6,7]]
This gif is demonstrating a color gradiation. The colors I chose for this are purple, color1 = [0.862, 0.643, 0.956] and green, color2 = [0.627, 0.933, 0.694]
The image below demonstrates a rotation around the z-axis by -90 degrees and no translation.
R = [[0, 1, 0], [-1, 0, 0], [0, 0, 1]]
T = [0, 0, 0]
This image below demonstrates a translation on the z-axis by 2 units.
R = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
T = [0, 0, 2]
This image below demonstrates a slight rotation around the y-axis and a translation in the y-axis of -0.5 units
R = [[cos(np.pi/30), 0, sin(np.pi/30)], [0, 1, 0], [-sin(np.pi/30), 0, cos(np.pi/30)]]
T = [0, -0.5, 0]
This image demonstrates a roation around the y-axis 90 degrees. We need a translation to make it seem that it's spinning in place even tho T0 was -3 in the z direction. So we translate -3 on the x-axis and 3 on the z-axis.
R = [[0, 0, 1], [0, 1, 0], [-1, 0, 0]]
T = [-3, 0, 3]
The below point clouds demonstrate the PC in view of the first camera, PC in the view of the second camera, and the PC of the combined clouds.
The image below represents the torus as a parametric function where the sampling size was 100.
The image below represents the torus as an implicit surface.The implicit surface representation of the torus took longer to render than the point cloud because it has to compute for every point along the surface. If we choose an infinitely large number of samples for the point cloud, we might recover something that looks like an implicit surface. But the main difference is that while there is a singular equation for the implcit surface, there is no way to solve for a point on the surface unlike for a parametric surface. You would need to use techniques like ray casting to sample from the surface and get a representation of each pixel in the 3D space. But with parametric functions, we can directly compute for points on the surface hence it is easier to render. Implicit surfaces are easier to change the topography of because there is no explicit representation. Another downfall of using point clouds is that we lose connectivity information where as this can be modeled by an implicit representation.
I call this "Disco Grazing". I used two new objects and had 2 instances of each for a total of 4 meshes that I combined into the scene using join_meshes_in_scene(). I also transformed the corrdinates so that the two trees and the two sheep would be in different locations. Additionally I scaled up the sheep so that it would not be too small in front of the trees. I used the coloring technique from part 3 to color the trees so they look like they have separation from the trunk to the leaves and alternated the color of the sheep between frames. Lastly, I changed the position of the light for a strobing disco effect.
The images below demonstrates sampling 10, 100, 1000, 10000 points on a mesh as well as the original mesh.
