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Computer Graphics 3 Cheat Sheet (DRAFT) by

Computer Graphics Turbo C

This is a draft cheat sheet. It is a work in progress and is not finished yet.

UNIT 3

PART A
three primary geometric elements
Vertex (Point), Edge (Line), Polygon (Face)
Quadric Surface
defined by second­-degree equations
polygon table
data structure storing lists of geometric and attribute data (to store connec­tivity inform­ation)
Plane equation
Ax+By+­Cz+D=0; x,y,z → components of normal vector
<0 inside; >0 outside
polygon meshes
Triangle and Quadri­lateral Meshes
spline
defined by a set of polynomial functions

Plane Equations in Rendering Pipeline

Back-Face Culling:
substitute viewport into plane equation (sign determines direction of plan for clipping)
Inside­-Ou­tside Testing & Depth:
if a point is inside a polygon; calculate depth of any point

Meshes

Polygon Meshes
Quadratic (or Parame­tric) Surfaces
made of triang­les­/quads
equati­ons­/co­ntrol points
Modelling Accuracy
Approx­imate, depends on number of polygons
High precision, smooth surfaces
Resource Requir­ements
Needs more memory for high detail
Compact repres­ent­ation, fewer parameters
Rendering Efficiency
Very efficient, directly supported by GPUs
Not directly render­able, must be converted to meshes
Ray surface inters­ection
Advantages
fast; basic algebraic math; comput­ation time predic­table; universal for any shape
exact repres­ent­ation; compact storage; analytical precision
Disadv­antages
approx­imation error; memory perfor­mance trade-off
comput­ational cost; specia­liz­ation required
Polygon meshes = standard for real-time rendering (fast, GPU-fr­iendly)
Quadratic surfaces = better for design accuracy, but used as pre-pr­oce­ssing before conversion to polygons
  

B-Spline and Bézier

B-Spline
Bézier
local control
global control
single compact repres­ent­ation
needs many separate curves
B-Splines are flexible, efficient (faster updates, less recomp­uta­tion) and manage­able.

Polygon tables

Geometric (Vertex) Table
Avoids duplic­ation
Attribute Table
Stores properties (color, texture, reflec­tivity)
Surface (Polygon) Table
Stores faces using vertex indices (geometry + attrib­utes)

Polygon tables

Geometric (Vertex) Table
Avoids duplic­ation
Attribute Table
Stores properties (color, texture, reflec­tivity)