Introduction to 3D Computer Graphics

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Fac. of Comp., Eng. Tech. Staffordshire
University
3D Computer Graphics
Introduction to 3D Computer Graphics
Dr. Claude C. Chibelushi
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Outline

• Definition
• Applications
• Typical Processing Steps
• Modelling and Rendering
• Typical Data Structures
• Summary

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Definition
3D graphics generally deals with graphical
display of 3D objects as seen by viewer
What is 3D Computer Graphics?
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Definition

• 3D graphics generation of graphical display
  (rendering) of 3D object(s) from specification
  (model(s))

Modelling
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Applications

• Computer graphics is used in many applications,
  e.g.
• Entertainment (computer games, movie special
  effects, ...)
• Human computer interaction (GUI, ...)
• Science, education, medicine (visualisation )
• Business (advertising, e-commerce, ...)
• Art

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Typical Processing Steps
Wireframe polygonal model
Solid object
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Typical Processing Steps
Modelling numerical description of scene
objects, illumination, and viewer
Rendering operations that produce view of scene
projected onto view surface
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Typical Processing Steps

• Loading or generation of object (shape, surface
  properties) model
• Model coordinate transformation translation,
  rotation, projection, ...
• Hidden surface removal
• Shading
• Display

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Modelling
1438 facets
Human Head Model
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Modelling
7258 facets
Human Head Model
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Modelling
2074 facets
Teacher and Board Model
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Rendering
Shaded Facets (Human Head)
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Rendering
1438 facets
Shaded Human Head
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Rendering
7258 facets
Shaded Human Head
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Rendering
Shaded Teacher and Board
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Rendering

• Scan conversion
• Rendering requires scan conversion
• Scan conversion of graphics primitive
• point-by- point traversal of primitive
• along (horizontal) scan lines
• coherence often exploited (e.g. incremental
  computation)
• reduces computational cost

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Rendering

• Scan conversion of filled polygons

Common approach polygon interior filled line by
line, one point at a time
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Rendering

• Scan conversion of filled polygons
• Determines points between pairs of intersections
  (scan-line / edges)
• Can be complex if no shape constraints
• polygon may be convex and concave
• many possible combinations of interior and
  exterior polygon regions

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Rendering

• Scan conversion of filled polygons
• General procedure
• find intersections of scan line with polygon edge
  (use equation of line joining two vertices)
• edge coherence, hence use incremental computation
• sort intersections left to right
• fill / shade / texture interior points between
  intersection pairs along scan line

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Rendering

• Scan conversion of filled polygons
• Generic algorithm requires
• interior / exterior tests
• tests for intersections shared by two edges
• tests for slivers
• edges so close that no or only one discrete point
  on scan-line segment
• (see Hearn Baker pp. 117 - 126)

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Rendering

• Scan conversion of filled triangles

P1 (x1, y1, z1)
P2 (x2, y2, z2)
P3 (x3, y3, z3)
(1) Sort vertices
(2) Split into two
(3) Fill sub-triangles
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Rendering

• Scan conversion of filled triangles
• scanConv3DTr(P1, P2, P3) / scan conversion of
  3D triangle /
• sort(P1, P2, P3) // descending y coordinate
  (y1 ? y2 ? y3)
• if (vertices on single line)
• return
• if (flat top or flat bottom)
• fillFlatTB3DTr(P1, P2, P3)
• else
• yf y2 // subdivide polygon into flat top
  / bottom triangles
• // (note also calculate xf, zf as required
  interpolation)
• fillFlatTB3DTr(P1, P2, Pf) // fill flat bottom
  sub-triangle
• fillFlatTB3DTr(P2, Pf, P3) // fill flat top
  sub-triangle

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Rendering

• Scan conversion of filled triangles
• fillFlatTB3DTr(Pa, Pb, Pc) / fill 3D triangle
  assumes ya? yb ? yc /
• if (flat bottom)
• calculate slope of edges PaPb and PaPc
• else
• calculate slope of edges PaPc and PbPc
• identify left and right edge
• for (each scan line between Pa and Pc)
• calculate edge intersections // to reduce
  cost, exploit edge coherence
• fill from left edge to right edge

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Data Structures

• Selection of data structures for computer
  graphics often driven by need for efficiency
• storage
• computation
• Trade-off between storage and computational
  efficiency often applied

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Data Structures

• Data structures are required for
• scene specification
• object, polygon, point / vertex, ...
• mathematical manipulations
• vector, matrix,
• graphical display
• buffer, ...
• Typical data structures trees / scene graphs,
  linked lists, arrays

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Data Structures
Linked list of objects
Linked lists of facets

• Computer graphics often use hierarchical data
  structures, e.g.

Linked lists of vertices

• Note
• other possible levels object groups, facet
  groups (surfaces), edges
• vertex may also link back to facets which share
  vertex (for shading)

Structures with x, y, z coordinates
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Data Structures

• Possible architecture

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Data Structures
/ 3D point or vertex with integer coordinates
/ typedef struct structTag3DiPoint
int xCoordinate, / x coordinate /
yCoordinate, / y coordinate /
zCoordinate / z coordinate /
int3DPoint, / 3D point /
pInt3DPoint, / pointer to a 3D point /
int3DVertex, / 3D vertex /
pInt3DVertex / pointer to a 3D vertex /

• Possible structure for 3D point or vertex

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Data Structures
/ Polygon in 3D space / typedef struct
structTag3DiPolygon int3DVertex i3SidedPoly3
int colour, visibilityFlag
float magNormal struct structTag3DiPolygon
link2NextPolygon / Other attributes can go
here / int3DPolygon, / 3D Polygon /
pInt3DPolygon, / pointer to a 3D Polygon /
int3DFacet, / 3D facet /
pInt3DFacet / pointer to a 3D facet /

• Possible structure for polygon

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Data Structures
/ Object in 3D space / typedef struct
structTag3DiObject pInt3DFacet pFacetList
pInt3DVertex pVertexArray int numVertices
int3DPoint worldPosition struct
structTag3DiObject link2NextObject / Other
attributes can go here / int3DObject,
/ 3D Object / pInt3DObject / pointer
to a 3D Object /

• Possible structure for 3D object

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Data Structures

• To cater for synthesis of copies of an object
• master / instance architecture
• master defines generic attributes of object
• instance defines attribute values of particular
  copy

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Data Structures
Instances
Masters
tm transf. matrix att attributes

• Possible architecture

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Suggested Reading

• Preface relevant parts of Ch. 2, A. Watt, 3D
  Computer Graphics, 3rd Ed., Addison-Wesley, 2000.
• Relevant parts of Ch. 1 2, D. Hearn, M.P.
  Baker, Computer Graphics, 2nd Ed. in C,
  Prentice-Hall, 1996.
• Relevant parts of Ch. 10, 11, 12, A. LaMothe,
  Black Art of 3D Game Programming, Waite Group
  Press, 1995.

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Suggested Reading

• J. Latta, A Look at the 3D Graphics Industry,
  Computer Graphics, Vol. 33, No. 3, pp. 18 - 21,
  1999
• C. Machover, Four Decades of Computer Graphics,
  IEEE Computer Graphics and Applications, Vol. 14,
  No. 6, pp. 14 - 19, 1994
• C. Machover, The Business of Computer Graphics,
  IEEE Computer Graphics and Applications, Vol. 20,
  No. 1, pp. 44-45, 2000
• N. Leavitt, 3D Technology Ready for the PC?,
  IEEE Computer, Vol. 34, No. 11 , pp. 17-20, 2001

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Summary

• 3D graphics
• deals with synthetic (graphical) representation
  of 3D information (typically a scene)
• most successful application of computer
  manipulation of images
• Processing pipeline transformations, hidden
  surface removal, shading,
• Selection of data structures (trees, lists,
  arrays, )
• often driven by computational and storage
  efficiency

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Summary

• Polygon fill
• common approach line by line, point by point
  traversal of polygon interior
• requires computation of line intersections, and
  sorting
• tests for special cases may be required
• triangle can be divided into flat top and flat
  bottom triangles
• coherence often exploited