Imaging

Modeling and Imaging Reality model Picture modeling Imaging (vizualisation)

Projection Mapping Φ: R n → R k n>k In case of 3D computer graphics Φ: R 3 → R 2 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.

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)

Axonometry Projection plane intersects coordinate axes dy dx dz

Dimetry Projection triangle is isiscelles

Izometry Projection triangle is equilateral (dx=dy=dz) Often also azimuth=zenith=45 o

Perspective Projection center is a point

1-vanishing point perpective

2-vanishing point perspective

3-vanishing point perspective

Wireframe „model“

Solving of edges visibility

Which faces are visible? The normal leads TO the observer → the face can (but must not) be visible The normal leads from the observer → the face is not visible

Painter’s algorithm Display the potentionaly visible faces from the back to the front

Painter’s algorithm The face is not visible

Painter’s algorithm The face can be visible

Painter’s algorithm The face is not visible

Painter’s algorithm The face can be visible

Painter’s algorithm The face is not visible

Painter’s algorithm The face can be visible

Painter’s algorithm The face is not visible

Painter’s algorithm The face is not visible

Painter’s algorithm The face can be visible

Painter’s algorithm The face can be visible

Counter example of painter’s algorithm

Simple imaging of all points of the solid

Rendering Light source observer Projection plane Angle α

Rendering

Light source types Point Point with directed lights (commonly cone shape) Area (commonly approximated by a matrix of points) Ambient

Ray Tracing Light sources Projection plane Mirror reflection Diffuse reflection The ray goes through the solid

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 tělesem –Directly (transparent solid) –With a shift –With a diffusion (translucent solid)

Ray Tracing

Radiosity E i = z i + o i * ∑v ij e j