DEFINING OBJECTS - 3D REPRESENTATIONS
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DEFINING OBJECTS - 3D REPRESENTATIONS
Surface representations
Polygon tables
3D curves and curved surfaces
Sweep representations
Constructive solid geometry
Octrees
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Two classes of representations
Surface
Solid
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Surface representations
• Polygon surfaces
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Surface representations
Object triangulation
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Succession of models
Wireframe Surface patch
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Surface patch Surface shading
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Surface representation
SurfaceVertex
Edge
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Vertices
V1
V2V3
V4
V5
V6 V7
V8
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Wire-frameV1
V2V3
V4
V5
V6 V7
V8
V1
V2V3
V4
V5
V6 V7
V8
V1
V2V3
V4
V5
V6 V7
V8
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Surface
V1
V2V3
V4
V5
V6 V7
V8
V2
V1
V2V3
V4
V5
V6 V7
V8
V2
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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
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Define vertex table(vertices and edges)
2 4 6 8
2
4
6
8
X
Y Z
2
V1 V2
V3V4
V5 V6
V7V8
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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
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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)
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Advanced representations for curves and curved surfaces (3D)
• parametric equations• Bézier curves and surfaces• splines and spline surfaces• B-splines• ß-splines• fractal surfaces
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Advanced representations for solids
• Sweep representations• Constructive Solid Geometry (CSG)• Octrees
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Sweep representations
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Sweep representations
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Constructive solid geometry
A B A - B A B
Volume = set of points
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Octrees
0 1
23
0 1 2 3
0 1 2 3
0 1 2 3
0 1
23
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Octrees
0 1
23
45
6
7
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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