Proseminar: WEB 3D

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Proseminar WEB 3D
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Proseminar Web 3D CG Fundamentals 3

• Hidden Surface Removal
• Lighting and Shading
• Texture Mapping

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Hidden Surface Removal
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Proseminar Web 3D CG Fundamentals 3

• Problem Given a set of 3D objects and a
  viewing specification, determine which lines or
  surfaces are invisible.
  
  
• Primitives outside of the field of view
• Back-facing primitives on a closed, convex object
• Primitives occluded by other objects closer to
  the camera

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Hidden Surface RemovalGeneral Approaches
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Proseminar Web 3D CG Fundamentals 3

• Image-Based Approach (Image Precision)
  
• for(each pixel in the image)
• determine the ray through the pixel
• determine the closest object along the
  ray
• draw the pixel in the color of the
  closest object
• 
  
• Object-Based Approach (Object Precision)
• for (each object in the world)
• determine unobstructed object parts
• draw the parts in the appropriate color

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Hidden Surface RemovalCoherence
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Proseminar Web 3D CG Fundamentals 3

• Objects typically have properties which vary
  smoothly
• Face coherence
• Edge coherence
• Scan line coherence
• Area coherence
• Depth coherence
• Frame coherence
• Object coherence
• Helps to avoid making expensive calculations, or
  to turn them into simple differences (like line
  drawing)

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Hidden Surface RemovalPerspective
Transformations
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Proseminar Web 3D CG Fundamentals 3

• Depth comparisons are typically performed after
  the perspective transformation
• Since were looking down the z axis, two points
  are now on the same ray if x1x2 and y1y2
• The perspective transformation preserves
• Relative depth
• Straight lines
• Planes

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Hidden Surface RemovalNormalizing the Viewing
Frustum
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Proseminar Web 3D CG Fundamentals 3

• Transform frustum to a cube before clipping -
  that is convert perspective frustum to
  orthographic frustum

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Hidden Surface RemovalHandling Occlusion
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Proseminar Web 3D CG Fundamentals 3

• Problem some polygons will overlap, therefore
  we must determine which portion of each polygon
  is visible to eye.

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Hidden Surface RemovalBack Culling
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Proseminar Web 3D CG Fundamentals 3

• Reduces complexity only
• Convex self-occlusion
• Angle between the viewing direction an the
  normal vector of a polygon to determine
  visibility
• Criterion vector product positive

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Hidden Surface RemovalBack To Front Sorting
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Proseminar Web 3D CG Fundamentals 3

• aka The Painter's method
• First Step The list of surfaces are sorted
  according to their distance from the viewpoint
• Second Step The objects are then painted from
  back-to-front.
• Criterion for polygon comparison simplest
  solution compare the maximum z coordinate

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Hidden Surface RemovalProblems with Painters
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Proseminar Web 3D CG Fundamentals 3

• Choosing a suitable sorting algorithm
• Bubble sort complexity O(n2)
• Radix sort complexity O(n)
• Quick sort complexity O(n lg n)
• The criterion of comparing the maximum z
  coordinate is not correct in general
• Mutual overlapping and piercing

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Hidden Surface RemovalConstructing a BSP Tree
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Proseminar Web 3D CG Fundamentals 3

• The Binary Space Partition (BSP) algorithm
• Select a partitioning plane/facet
• Partition the remaining planes/facets according
  to the side of the partitioning plane that they
  fall on ( or -)
• Repeat with each of the two new sets
• In the case of a crossing facet we clip it into
  two halves

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Hidden Surface RemovalComputing Visibility with
BSP Trees
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Proseminar Web 3D CG Fundamentals 3

• Starting from the root of the tree
• Classify viewpoint as being in the positive or
  negative half-space of our plane
• Call this routine with the opposite half-space
• Draw the current partitioning plane
• Call this routine with the same half-space

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Hidden Surface RemovalPixel-level Visibilty
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Proseminar Web 3D CG Fundamentals 3

• Thus far - visibilty at the level of primitives
• Now - visibilty at the level of each pixel

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Hidden Surface RemovalRay Casting
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Proseminar Web 3D CG Fundamentals 3

• A very general algorithm
• Works with any primitive we can write
  intersection tests for
• but it's hard to make it run fast
• And thats why
• can use it for much more than visibility testing
• shadows, refractive objects, reflections, motion
  blur,...

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Hidden Surface RemovalScanline Visibilty
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Proseminar Web 3D CG Fundamentals 3

• Looks a lot like polygon rasterization
• Maintains active object table
• Looks at one scanline at a time - no need to
  store entire image - nice if memory scarce

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Hidden Surface RemovalDepth (Z) Buffering
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Proseminar Web 3D CG Fundamentals 3

• Project all primitives and update depth of each
  pixel
• set depth of all pixels to ZMAX
• for (each primitive in the screen)
  determine pixels touched
• for (each pixel in the primitive)
• compute z at pixel
• if (zlt depth)
• pixel object color
• depthz

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Hidden Surface RemovalLooking at Depth (Z)
Buffering
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Proseminar Web 3D CG Fundamentals 3

• Pros
• Any kind of primitives - not just planar polygons
• Simple and well suited to H/W implementation
• Spatial coherence - determination of z coordinate
  by linear interpolation
• Primitives can be processed in any order
• Cons
• Excessive over-drawing
• Doesn't handle transparency well
• Needs intelligent selection of znear zfar
  clipping planes

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Illumination and ShadingIllumination Models
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Proseminar Web 3D CG Fundamentals 3

• Illumintaion
• Lightning
• Shading
• Illumination Models

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Illumination and ShadingTwo Components of
Illumination
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Proseminar Web 3D CG Fundamentals 3

• Light Sources (Emitters)
• Emission Spectrum (colour)
• Geometry (positional and directional)
• Directional Attenuation
• Surface Properties
• Reflectance Spectrum (colour)
• Geometry (position, orientation, and
  micro-structure
• Absorption

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Illumination and ShadingLight Sources
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Proseminar Web 3D CG Fundamentals 3

• Ambient Light Sources
• No spatial or directional characteristics
• Independent of object's position and orientation
• Directional Light Sources
• All rays have common direction
• Example sunlight
• Spot Light Sources
• Emits rays in a radial direction from its source
• Example light bulb
• Other Light Sources

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Illumination and ShadingDiffuse Reflection and
Lighting
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Proseminar Web 3D CG Fundamentals 3

• Ideal Diffuse Reflection
• A very rough surface on microscopic level
• Example chalk
• Lambert's Cosine Law
• How much of the incoming light energy is
  reflected
• Computing Diffuse Refelection

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Illumination and ShadingSpecular Reflection and
Lighting
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Proseminar Web 3D CG Fundamentals 3

• Ideal Specular Reflection
• A very smooth surface on microscopic level
• Example mirror
• Snell's Law
• Non-ideal Reflectors
• Empirical model

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Illumination and ShadingPhong Illumination
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Proseminar Web 3D CG Fundamentals 3

• The Phong Illumination Model
• Phong Examples
• Variable direction of the light source and
  shininess coefficient

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Illumination and ShadingSimple Shading
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Proseminar Web 3D CG Fundamentals 3

• Flat Shading
• A only one illumination calculation for each
  primitive
• Facet Shading
• Apply illumination equation at each point

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Illumination and ShadingGouraud Shading
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Proseminar Web 3D CG Fundamentals 3

• First applies the illumination model one subset
  of surface points
• Then interpolates the intensity of the
  remaining points on the surface
• But the facet artefacts are still visible

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Illumination and ShadingPhong Shading
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Proseminar Web 3D CG Fundamentals 3

• Based on Goraud Shading
• First the surface normal is linearly
  interpolated across polygonal facets
• Then the illumination model is applied at every
  point

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Illumination and ShadingAdvanced Lighting and
Shading
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Proseminar Web 3D CG Fundamentals 3

• Physically Based Illumination Models
• use parameters that have clear physical analogies
  
• predictive
• Recursive Ray Casting
• Radiosity
• Uses the theory of heat transfer

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Texture MappingThe Quest for Visual Realism
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Proseminar Web 3D CG Fundamentals 3

• At what point do things start to look real ?
• Photo Texture

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Texture MappingHow to do it ?
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Proseminar Web 3D CG Fundamentals 3

• Image space scan
• samples the warped texture at the appropriate
  image pixel
• May miss parts of the texture
• Texture space scan
• places each texture sample to the mapped image
  pixel
• May not fill imageForward

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Texture MappingProblems
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Proseminar Web 3D CG Fundamentals 3

• Problem 1 fitting - we deal with non-liner
  transformations
• Problem 2 mapping form a pixel to texel -
  aliasing

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Texture MappingHow to do it ?
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Proseminar Web 3D CG Fundamentals 3

• MIP Mapping
• prefiltering technique we apply it before
  texture mapping (rasterization)
• BUMP Mapping
• alters the surface normal of an object
• the actual shape of the object does not change