EXPLANATION

Major Concepts and Tools used

• C programming

  • Libraries

• Mathematics

  • Parametric(torus)
  • 3-D Geometry
  • rotational matrices

• Terminal & display tools

  • ANSI escape codes(\x1b[2j,\x1b[h) : clear screen and move cursor to top-left to render new frames in-place.
  • Terminal emulator — the characters, width/height and font affect perceived aspect ratio
  • memset : for fast clearing

• Rendring technique & algorithms

  • Z-buffer(depth buffer) ->z[0] prevents farther points from overwriting nearer ones.
  • ASCII shading(.,-~:;=!*#$@)

Short concept (overview)

• Parametric torus → two angles (θ, φ).

• Rotate → apply rotation matrices (or algebraic equivalent).

• Project → divide x,y by depth to produce perspective.

• Shade → dot(normal, light_dir) → char ramp.

• Z-buffer → keep closest D per cell.

• Performance → precompute, small memory, optimize compiler flags.