1 polygonal techniques 2002. 5. 15 이영건. 2 introduction this chapter –discuss a variety of...
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Polygonal TechniquesPolygonal TechniquesPolygonal TechniquesPolygonal Techniques
2002. 5. 15 2002. 5. 15
이영건이영건
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Introduction
• This chapter– Discuss a variety of problems that are
encountered within polygonal data sets
• The goal for polygonal representation– Accuracy and speed
• The three topic– Tessellation, consolidation, simplification
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Term definition
• Tessellation– Polygonal of the different forms have to
split into more tractable primitives• Displayed correctly
• Consolidation– The process which encompasses merging
and linking polygonal data• Improve data display
• Simplification– Attempting to remove unnecessary or
insignificant features• More speed
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Three-Dimensional Data - 1
• Deferent representation for deferent types of objects– Solid-base modelers
• Voxels (fig – a)• Constructive solid geometry (fig – b)
Fig - a
Fig - b
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Three-Dimensional Data - 2
– Surface-base modelers• Mesh (fig – b)• Subdivision (fig – c)• Parametric surface (fig – a)• Implicit surface
– f(x, y, z) = 0
Fig - b Fig - cFig - a
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Tessellation - 1
• Tessellation– The process of splitting a polygon into a set of
polygons
• Reasons– Triangle : optimization for Many graphics APIs and
hardware (triangulation)– Renderer : handling convex polygons (convex
partitioning)– In order to catch shadows and reflected light
The different types of tessellation
(b. convex partition, c. triangulation, d. uniformly meshed)
a b c d
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Tessellation - 2
• Process of tessellation– How best to project a three-dimensional
polygon into two dimensions• Best plane
– Selection the largest projected area among the xy, the yz, the zx
– Using the greatest magnitude in the polygonal’s normal
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Tessellation - 3
– Problems• Polygon facets by creating the modelers can be
badly warped – produce an hourglass or bowtie quadrilateral
(fig-a)– Using line / line intersection test (section 10.12)
• Polygons are not always made of a single outline– Using the join edge (fig-b)
Fig - aFig - b
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Shading problems
• Split the quadrilateral into the triangles – Provide proper input to the renderer– Avoid bowtie problems– Notice
• Select the good diagonal edge for renderer
• The different ways – Using the minimized differences (between color)
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Shading problems
• The different ways– Using the diagonal that gives the largest angle
between the two triangles
Left : each quadrilateral split along the same diagonal
Right : the split is made using the diagonal whose corners are
closer in height
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Shading problems
• Problem of warped quadrilateral– Texture is applied – When tessellation apply, distort texture – Requirement
• Fine meshing of surface• Use texture-coordinate interpolation scheme
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Edge cracking and T-Vertices
• Producing the NURBS by modeler – Happen the edge cracking at the shared edge by the
two surface
– Solution• Edge stitching
– When joining flat surface is that of T-vertices, happen to related problem
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Consolidation
• Consolidation– To find and adjust the links between polygons for
rendering
• Advantage – Improve efficiency
• The display polygon meshes• The area of backface culling
• Quality-related problem– Face orientation
• Use a right-handed orientation (counter-clockwise direction)
Problem : When model has the only surface normal.
Left : don’t have the normal per vertex
Right : have the normal per vertex
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Consolidation
Solution for forming polygonal meshes 1. Form edge-face structure 2. Find groups of polygons (determine solidity)3. For each group, flip faces to gain consistency4. Determine what the inside of the mesh is 5. Find smoothing groups and compute vertex
normals6. Find boundaries7. Create polygonal meshes
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Consolidation
– Form edge-face structure• Form a list of all edges in the entire set of polygons• Sorting by vertex coordinates • Ex) v1(-3,5,2), v2(-3,6,-8) v1 => v2 sorting
– Find groups of polygons (determine solidity)• A group consist of polygons which are connected by
edges• Ex) two group of the teapot : the pot and the lib
– For each group, flip faces to gain consistency• Ensure orientation consistency (counter-clockwise
outlines)• Select an arbitrary starting polygon• Traversal neighbor polygons• No consistency, apply flipping
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Simplification - 1
• Simplification– The process of taking a complex model and
reducing complexity – Data reduction or decimation
• The main advantage – Be quicker to render
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Simplification - 2
• The operation of simplification– Edge collapse
• The strategy for new vertex placement– Select one vertex or the other vertex [Melax]
• Faster, Lower-quality – Check the midpoint on the edge [Hoppe]– Check both vertices on the edge [Garland and
Heckbert]• Higher-quality, Extra processing, code and momory
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Simplification - 3
• Problem of edge collapse– Happen to edge crossing– Solution
• Using of the best cost function
– Happen to ambiguous edge collapse
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• The extension of the cost function– by Garland and Heckbert– Be to weight the value by the areas of the triangles
associated with each plane– Be to use a cost function based on maintaining other
surface features – Be to preserve the material changes, texture map
edges, color-per-vertex changes
Simplification - 4
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Simplification - 5
• The simplification of LOD– Problem
• Happen to “Popping effect”
– Solution• Be to use alpha blending to cross-fade between
model representation• Be to use geomorphs to increase or decrease the
level of detail