3D Graphics by Hand: Vertex Tables, Rotations, Camera Space, Perspective Projection, Screen Mapping, Back-Face Culling, Depth Buffers & Flat Shading

What you'll build

What you will be able to do

Each lab ends with a concrete result that you build yourself and the checker confirms, cell by cell.

• Store a toy cube as a vertex table and a face table, measure edges and diagonals with INDEX lookups, find each face's centre and the bounding box, and see why shared vertices keep a mesh small.
• Scale the cube, rotate it about the z-axis with SIN, COS and RADIANS, move it into place, and then turn one point about two axes in both orders to see that the results differ.
• Subtract the camera position from every world point, turn the offsets by the camera's yaw, flag points that lie behind the camera and count what is left in front.
• Turn the field of view into a focal factor, divide by depth to project every point, correct x for the wide screen and flag points outside the near and far planes.
• Stretch NDC values onto a 640 × 360 viewport, round them to whole pixels, flip y because pixel rows count downwards, flag a point off the screen and plot the projected cube.
• Build two edge vectors per face from its pixel corners, take the z of their cross product as a signed area, mark faces as facing or culled and measure how much work culling saves.
• Count the fragments that land on each pixel, keep the nearest depth with MINIFS, look up which face is visible with INDEX/MATCH and measure the overdraw.
• Light each face with the dot product of its normal and the light direction, turn that into a grey level with an ambient share, chart the shading and check whether the whole frame fits a 30 or 60 frames-per-second budget.