defining objects - 3d representations
DESCRIPTION
DEFINING OBJECTS - 3D REPRESENTATIONS. Surface representations Polygon tables 3D curves and curved surfaces Sweep representations Constructive solid geometry Octrees. Two classes of representations. Surface. Solid. Surface representations. Polygon surfaces. Surface representations. - PowerPoint PPT PresentationTRANSCRIPT
DEFINING OBJECTS - 3D REPRESENTATIONS
Surface representations
Polygon tables
3D curves and curved surfaces
Sweep representations
Constructive solid geometry
Octrees
Two classes of representations
Surface
Solid
Surface representations
• Polygon surfaces
Surface representations
Object triangulation
Succession of models
Wireframe Surface patch
Surface patch Surface shading
Surface representation
SurfaceVertex
Edge
Vertices
V1
V2V3
V4
V5
V6 V7
V8
Wire-frameV1
V2V3
V4
V5
V6 V7
V8
V1
V2V3
V4
V5
V6 V7
V8
V1
V2V3
V4
V5
V6 V7
V8
Surface
V1
V2V3
V4
V5
V6 V7
V8
V2
V1
V2V3
V4
V5
V6 V7
V8
V2
Vertex table
VERTEX TABLE
V1: x1 y1 z1V2: x2 y2 z2V3: x3 y3 z3V4: x4 y4 z4V5: x5 y5 z5V6: x6 y6 z6V7: x7 y7 z7V8: x8 y8 z8
EDGE TABLE
E1: V1 V2E2: V2 V3E3: V3 V4E4: V4 V1E5: V5 V6E6: V6 V7E7: V7 V8E8: V8 V5E9: V1 V5E10: V2 V6E11: V3 V7E12: V4 V8
SURFACE TABLE
S1: E1 E2 E3 E4S2: E5 E6 E7 E8S3: E1 E10 E5 E9S4: E2 E11 E6 E10S5: E3 E12 E7 E11S6: E4 E9 E8 E12
Define vertex table(vertices and edges)
2 4 6 8
2
4
6
8
X
Y Z
2
V1 V2
V3V4
V5 V6
V7V8
Consistency checking
• every vertex is listed as an endpoint of at least two lines
• every polygon is closed• each polygon has at least one shared edge• if edge table contains pointers to polygons
Hierarchical definitions
– interaction: groups of primitives can be interactively manipulated together, irrespective of a method of construction.
– storage efficiency: definition of repeated symbol needs to be stored only once
– common visual properties: groups of primitives can be given the same attributes, for example colour, transparency, visibility etc.
– common transformation: groups of primitives can be all transformed together (for example rotated)
Advanced representations for curves and curved surfaces (3D)
• parametric equations• Bézier curves and surfaces• splines and spline surfaces• B-splines• ß-splines• fractal surfaces
Advanced representations for solids
• Sweep representations• Constructive Solid Geometry (CSG)• Octrees
Sweep representations
Sweep representations
Constructive solid geometry
A B A - B A B
Volume = set of points
Octrees
0 1
23
0 1 2 3
0 1 2 3
0 1 2 3
0 1
23
Octrees
0 1
23
45
6
7
Define vertex table(vertices and edges)
2 4 6 8
2
4
6
8
X
Y Z
2
V1 V2
V3V4
V5 V6
V7V8
V11 V12
V13
V14
V15 V16
V17V18
V9
V19
V20
V10