Vertex Processing - Introduction to Computer Graphics - Lecture Slides, Slides of Computer Graphics

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Vertex Processing:

Viewing

Rendering Pipeline

• OpenGL rendering works like an assembly

line

• Each stage of the pipeline performs a distinct function on the data flowing by
• Each stage is applied to every vertex to determine its contribution to output pixels Geometry (Vertices) Vertex Processing Rasterizer Fragment Processing Pixels

Vertex Processing

• Vertex processing consists of:
  • ModelView transform
  • Projection transform
  • Lighting
  • Perspective divide
  • Polygon clipping
  • Viewport transform Vertex Processing

Vertex Processing

Vertex Processing

Vertices

Modelview Transform Projection Transform Clipping & Primitive Assembly Viewport Transform Lighting

Viewing in OpenGL

• The OpenGL viewpoint acts as a virtual

camera

• What parameters do you need to define a camera? - Viewpoint (Center of Projection) - View direction - Field of view - Film size - Projection plane

Viewing

• Viewing requires 3 elements:
  • Objects to be viewed
  • A viewer with a projection surface
  • A projection from the objects to the viewing surface

Viewing

• Example: OpenGL camera
  • Objects: The input geometry
  • Viewer: The OpenGL “camera” (with the view volume as its viewing “surface”)
  • Projection: The OpenGL projection matrix (GL_PROJECTION), maps 3D space (world coordinates) into 3D space (eye coordinates) - Eventually into normalized device coordinates (NDC)

Classical Viewing

• Classical views are based on the relationship

between these 3 elements: objects, a

viewer, and a projection

• In classical views, objects are assumed to be

constructed from flat principal faces

• i.e. many buildings
• Used primarily by architects / engineers

Perspective vs. Parallel

• Perspective
  • Viewing volume is a truncated pyramid
    • aka frustum
• Orthographic
  • Viewing volume is a box

Perspective

Orthographic

Taxonomy of Planar Geometric

Projections

Planar Geometric Projections

Perspective

Parallel / Orthographic

Multiview Axonometric Oblique

Isometric Dimetric Trimetric

One-point Two-point Three-point

Benefits

• Why use orthographic?
  • Preserves distances and angles
    • Perspective does not
  • Can be used for measurements
• Why multiview?
  • The main problem with orthographic projection is that it hides many surfaces
  • Often add isometric view as well

Axonometric Projections

• Direction of projection is still perpendicular

to the viewing plane

• But principle faces not parallel to it
• 3 different kinds:
• Isometric, dimetric, trimetric
• Classified by number of different foreshortening factors

Advantages and Disadvantages

• Advantages:
  • Can see multiple faces of an object simultaneously
  • Lines are scaled, but by a constant factor
    • Could still be used for measurement
• Disadvantages:
  • Angles not preserved
  • Foreshortening does not depend on distance - Not realistic

Oblique Projection

• Direction of projection is not

perpendicular to the viewing plane

• Most general parallel projection
• Is this possible with a normal camera?