Topics for Exam_02
 Topics
  • Coordinate systems (2D and 3D Coordinate)
  • Points and Vectors in 2d and 3d coordinates
  • Points and vectors in 2d and 3d homogenous coordinates
  • Matrices
    • Addition, multiplication, identity matrix, matrix inverse
  • Vectors
    • Length, normalization, inner product
  • Transformations
    • Mapping from window to viewport 
    • 2d and 3d translations, rotation, scale, and shear
    • Composite transforms
      • Align a vector with a coordinate axis
      • Rotate objects around an arbitrary 3D line or axis
      • Align a coordinate system with the world coordinate system
  • Lines and planes
    • Parametric equations of lines
    • Equation of planes: given 3 points, given a point on the plane and plane normal
  • Viewing in 3-dimensional space
    • Steps to perform parallel projections in 3d space and clipping against parallel view volume.
    • Steps to perform perspective projections in 3d space and clipping against perspective view volume.
  • Curves
    • General Parametric nth Order Curves: Represented as: C(t)=G⋅M⋅T
      • G is the geometry vector, M is the characteristic matrix, and T is the basis vector
      • G: Contains control points defining the curve.
      • Characteristic matrix M encodes the curve type (e.g., Hermite or Bezier)...
    • Tangent vectors: Tangents describe the direction of the curve at any given point.
    • Finding geometry vector and characteristic matrix for general nth order curves.
    • Finding coefficients for general nth order curves.
    • Finding blending functions for general nth order curves.
  • Surfaces
    • Parametric surfaces: Bilinear ; Biquadratic ; Bicubic ; Mixed types (e.g., cubic-linear, cubic-quadratic).
    • Calculation of tangent vectors and normal vectors on surfaces.
    • Finding characteristic matrix, geometry matrix, coefficients matrix, and blending surfaces for Hermite, Bezier, and Mixed types (e.g., cubic-linear, cubic-quadratic)
  • Colors
    • Intensities, CIE chromaticity diagram, RGB, HSV, and CMYK
  • Illumination and Shading
    • Ambient, Diffuse, Specular components
    • Polygon shading: Constant shading, Gouraud shading, Phong shading
  • Ray Tracing
    •  Ambient, diffuse, and specular lighting calculations.
    • Ray equation from camera to pixels 
    • Calculation of surface normal, reflected rays, shadow rays
    • Intersection Calculations: Ray-plane, ray-sphere, ray-triangle and Barycentric coordinates.
 
 
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