Zobrazov

1
Imaging
2
Modeling and Imaging
Picture
model
Reality
modeling
Imaging (visualisation)
3
Projection

• Mapping F Rn? Rk ngtk
• In case of 3D computer graphics F
  R3? R2
• Projection ray
• The set of all pictures with the same image
• Projection ray is usually a line
• The image is in the intersection of the
  projection ray and the projection plane.

4
Parallel projection

• Intersection of projection rays (projection
  center) is in the infinity
• Projection rays are parallel
• Their direction is defined by two angels
  (azimuth,zenith)

5
Parallel projection

• Intersection of projection rays (projection
  center) is in the infinity
• Projection rays are parallel
• Their direction is defined by two angels
  (azimuth,zenith)

6
Axonometry

• Projection plane intersects coordinate axes

dy
dx
dz
7
Dimetry
Projection triangle is isiscelles
8
Izometry

• Projection triangle is equilateral (dxdydz)

Often also azimuthzenith45o
9
Perspective

• Projection center is a point

10
1-vanishing point perpective
11
2-vanishing point perspective
12
3-vanishing point perspective
13
Wireframe model
14
Solving of edges visibility
15
Solving of edges visibility
16
Which faces are visible?
The normal leads from the observer ? the face is
not visible
The normal leads TO the observer ? the face can
(but must not) be visible
17
Painters algorithm

• Display the potentionaly visible faces from the
  back to the front

18
Painters algorithm
The face is not visible
19
Painters algorithm
The face can be visible
20
Painters algorithm
The face is not visible
21
Painters algorithm
The face can be visible
22
Painters algorithm
The face is not visible
23
Painters algorithm
The face can be visible
24
Painters algorithm
The face is not visible
25
Painters algorithm
The face is not visible
26
Painters algorithm
The face can be visible
27
Painters algorithm
The face can be visible
28
Counter example of painters algorithm
29
Simple imaging of all points of the solid
30
Rendering
observer
Light source
Projection plane
Angle a
31
Rendering
32
Light source types

• Point
• Area (commonly approximated by a matrix of
  points)
• Ambient

33
Ray Tracing
Mirror reflection
Light sources
Projection plane
Diffuse reflection
The ray goes through the solid
34
Types of reflection on the solid

• The ray is absorbed by a solid (solid color)
• The ray is reflected
• Mirror reflection (shine)
• Diffuse reflection
• Combinated reflection
• The ray is going through the solid telesem
• Directly (transparent solid)
• With a shift
• With a diffusion (translucent solid)

35
Ray Tracing
36
Radiosity

• e1 z1 o1 ? jv1jej
• e2 z2 o2 ? jv2jej
• ei zi oi ? jvijej