Seminars

• Academic principles
• 5 homework assignments: 50 points (10 points each) + bonus points
  • All assignments must be accepted
  • Later submissions are penalized by 3 points for each week of delay!
• Test in the 12th week for up to 10 points
• At least 30 points for the assessment

• Simple graphics library (SGL) divided into 5 assignments
• Team of two people (possibly across all course parallels, if need be)
• Submission:
  • Automatic & manual evaluation: https://cw.felk.cvut.cz/brute/
    • Images diff
    • Speed competition
    • Clean build & run
    • Clear code, comments, etc.
    • Functionality
• Speed competition (homework assignments I, II, III):
  • 3 bonus points for the 1st fastest solution
  • 2 bonus points for the 2nd fastest solution
  • 1 bonus point for the 3rd fastest solution

• Test application using GLUT for all homework assignments: sgl+testapp.zip
  • Use CMake to generate makefile or VS solution
    • New: using CMake variable SGL_BACKEND, you can choose to code either in the C++ (the default), Rust, or Zig language
  • Windows: freeglut binaries are part of the zip file
  • Linux/MacOS: GLUT installation (e.g. freeglut using brew)
• Test application calls SGL functions declared in sgl-{cpp,rust,zig}/include/sgl.h, that is the fixed interface of SGL
• Implement functions in sgl-{cpp,rust,zig}/src/*
• Switch contexts using keys 0-9
• SGL API documentation

Presentation

• Library initialization, data structures design
• Rasterization of basic primitives:
  • Point
  • Line and polyline (Bresenham's algorithm)
  • Circle (Bresenham's algorithm)
  • Ellipse (sglEllipse) and arc (sglArc):
    • Approximation of ellipse by 40 line segments
    • Approximation of arc by 40*(from-to)/(2 PI) line segments
    • BONUS:
      • Adaptive approximation of ellipse and arc with the error less than 1 pixel (1 point)
• Transformations:
  • Modeling transformations (translation, rotation, scale)
  • Orthographic projection (sglOrtho)
  • Viewport transformation
  • Transformation stack

graphics elements

transformations

transformation stack

Presentation

• Non-convex polygon filling:
  • Polygon definition (sglBegin(SGL_POLYGON))
  • Self-intersecting polygon filling, so don't use seed filling!
• Filling circle, ellipse, and arc
• Perspective projection (sglFrustum)
• Depth management via z-buffer
• BONUS:
  • Perspective correct interpolation of vertex attributes (1 point)

non-convex polygon filling

graphics elements filling

3D scene rendering - cube with z-buffer enabled/disabled

3D scene rendering - NFF file

Presentation

• Scene definition via SGL API (see sgl.h)
• Primary rays generation:
  • Transformation matrix inverse
  • Matrix inverse from Numerical Recipes in C
• Ray-sphere intersection
• Ray-triangle intersection: Moeller or PBRT
• Phong lighting model:
  • Material definition (see sglMaterial)
  • Diffuse coefficients: [r*kd g*kd b*kd]
  • Specular coefficients: [ks ks ks]
• BONUS:
  • Adaptive anti-aliasing (1 point),
  • Multiple lighting models support: Cook-Torrance or Ward (1 point)

sphere

Cornell box

sphere on floor

Presentation

• Shadow rays
• Secondary Rays: recursive ray tracing:
  • Reflections and refractions
  • Max. recursion depth 8
• Backface culling: ignore intersections if DotProd(normal,dir)>0.0
• BONUS:
  • Depth of field (1 point)

shadows

reflections and refractions

multiple reflections and refractions

Presentation

• Area light sources:
  • Emissive materials support (see sglEmissiveMaterial)
  • Point sampling on triangles, 16 samples per triangle
  • Intensity of light samples (Phong lighting model):
    • sample_i = (r,g,b)*cos fi*(light_triangle_area/num_samples)/(c0 + c1*d + c2*d^2)
    • cos fi = DotProd(light_triangle_normal, -shadow_ray.direction)
• Environment mapping:
  • Use environment map instead of constant background color (see sglEnvironmentMap)
  • Mapping ray direction to environment map coordinates (u,v) [0,1]x[0,1]:
    • d = sqrt(dir.x^2 + dir.y^2)
    • r = d>0 ? acos(dir.z)/(2*PI*d) : 0.0
    • u = 0.5 + dir.x * r
    • v = 0.5 + dir.y * r
• BONUS:
  • Textures support (2 points)

area light source

color area light source

environment map St. Peter's Basilica
(stpeters_probe.hdr)

environment map St. Uffizi Gallery
(uffizi_probe.hdr)