06b rendering iii

7/27/2019 06b Rendering III

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& Shading

Thomas FunkhouserPrinceton UniversityC0S 426, Fall 1999

2008'

3D PolygonRendering Pipeline

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3D Rendering Pipeline (for direct illumination)3D Primitives

ModelingTransformation

ProjectionTransformation

Clipping

Lighting

Image

ViewportTransformation

ScanConversion

2D Image Coordinates

3D Modeling Coordinates

3D World Coordinates

3D Camera Coordinates

2D Screen Coordinates


ViewingTransformation



Scan Conversion& Shading

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Overview Scan conversion

Figure out which pixels to fill

ShadingDetermine a color for each filled pixel

Texture MappingDescribe shading variation within polygon interiors

Visible Surface DeterminationFigure out which surface is front-most at every pixel

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Scan Conversion Render an image of a geometric primitive

by setting pixel colors

Example: Filling the inside of a triangle

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void SetPixel(int x, int y, Color rgba)

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Scan Conversion Render an image of a geometric primitive

by setting pixel colors

Example: Filling the inside of a triangle

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void SetPixel(int x, int y, Color rgba)

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Triangle Scan Conversion Properties of a good algorithm

SymmetricStraight edgesAntialiased edgesNo cracks between adjacent primitivesMUST BE FAST!

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Triangle Scan Conversion Properties of a good algorithm

SymmetricStraight edges

Antialiased edgesNo cracks between adjacent primitivesMUST BE FAST!

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Simple Algorithm

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void ScanTriangle(Triangle T, Color rgba){for each pixel P at (x,y){

if (Inside(T, P))SetPixel(x, y, rgba);

}}

Color all pixels inside triangle

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Inside Triangle Test A point is inside a triangle if it is in the

positive halfspace of all three boundary linesTriangle vertices are ordered counter-clockwisePoint must be on the left side of every boundary line

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Inside Triangle TestBoolean Inside(Triangle T, Point P){

for each boundary line L of T {Scalar d = L.a*P.x + L.b*P.y + L.c;if (d < 0.0) return FALSE;

}return TRUE;

}

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Simple Algorithm

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void ScanTriangle(Triangle T, Color rgba){for each pixel P at (x,y){

if (Inside(T, P))SetPixel(x, y, rgba);

}}

What is bad about this algorithm?

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Triangle Sweep-Line Algorithm Take advantage of spatial coherence

Compute which pixels are inside using horizontal spansProcess horizontal spans in scan-line order

Take advantage of edge linearityUse edge slopes to update coordinates incrementally

dxdy


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Triangle Sweep-Line Algorithmvoid ScanTriangle(Triangle T, Color rgba){

for each edge pair {initialize x L, x R ;compute dx L/dy L and dx R /dy R ;for each scanline at y

for (int x = x L; x


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Polygon Sweep-Line Algorithmvoid ScanPolygon(Triangle T, Color rgba){

sort edges by maxy make empty active e dge list

for each scanline (top-to-bottom) {insert/remove edges from active edge listupdate x coordinate of every active edgesort active edges by x coordinatefor each pair of active edges (left-to-right)

SetPixels(x i , x i+1 , y, rgba);}

}

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Hardware Scan Conversion Convert everything into triangles

Scan convert the triangles

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Hardware Antialiasing Supersample pixels

Multiple samples per pixelAverage subpixel intensities (box filter)Trades intensity resolution for spatial resolution

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Shading How do we choose a color for each fi lled pixel?

Each illumination calculation for a ray f rom the eyepointthrough the view plane provides a radiance sample How do we choose where to place samples? How do we filter samples to reconstruct image?

Angel Figure 6.34

Emphasis on methods that canbe implemented in hardware

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Ray Casting Simplest shading approach is to perform

independent lighting calculation for every pixelWhen is this unnecessary?

))()((i i

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iS ii D AL A E I RV K I L N K I K I I


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Polygon Shading Can take advantage of spatial coherence

Illumination calculations for pixels covered by sameprimitive are related to each other

))()((i i

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Polygon Shading Algorithms Flat Shading

Gouraud Shading

Phong Shading

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Flat Shading What if a faceted object is il luminated only by

directional light sources and is either diffuse orviewed from infinitely far away

))()((i i

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Flat Shading One illumination calculation per polygon

Assign all pixels inside each polygon the same color

N

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Flat Shading Objects look like they are composed of polygons

OK for polyhedral objectsNot so good for ones with smooth surfaces

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Gouraud Shading Phong Shading


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Gouraud Shading What if smooth surface is represented by

polygonal mesh with a normal at each vertex?

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Watt Plate 7

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Gouraud Shading Method 1: One lighting calculation per vertex

Assign pixels inside polygon by interpolating colorscomputed at vertices

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Gouraud Shading Bilinearly interpolate colors at vertices

down and across scan lines

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Gouraud Shading Smooth shading over adjacent polygons

Curved surfacesIllumination highlightsSoft shadows

Mesh with shared normals at verticesWatt Plate 7

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Gouraud Shading Produces smoothly shaded polygonal mesh

Piecewise linear approximationNeed fine mesh to capture subtle lighting effects

Gouraud ShadingFlat Shading

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Gouraud Shading Phong Shading


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Phong Shading What if polygonal mesh is too coarse to capture

illumination effects in polygon interiors?

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Phong Shading One lighting calculation per pixel

Approximate surface normals for points inside polygonsby bilinear interpolation of normals from vertices

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Phong Shading Bilinearly interpolate surface normals at vertices

down and across scan lines

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Polygon Shading Algorithms

Gouraud Phong

Wireframe Flat

Watt Plate 7

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Shading Issues Problems with interpolated shading:

Polygonal silhouettesPerspective distortionOrientation dependence (due to bilinear interpolation)Problems at T-verticesProblems computing shared vertex normals

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SurfaceImageTexture

Textures Describe color variation in interior of 3D polygon

When scan converting a polygon, vary pixel colorsaccording to values fetched from a texture

Angel Figure 9.3 T h o m a s

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Surface Textures Add visual detail to surfaces of 3D objects

Polygonal model

With surface texture

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Surface Textures

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3D Rendering Pipeline (for direct illumination)3D Primitives

ModelingTransformation

ProjectionTransformation

Clipping

Lighting

Image

Viewport

Transformation

ScanConversion


3D Modeling Coordinates


3D Camera Coordinates



ViewingTransformation



Texture mapping

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Overview Texture mapping methods

MappingFilteringParameterization

Texture mapping applicationsModulation texturesIllumination mappingBump mappingEnvironment mappingImage-based renderingNon-photorealistic rendering

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Texture Mapping Steps:

Define textureSpecify mapping from texture to surfaceLookup texture values during scan conversion

(0,0)

(1,0)

(0,1)

uv

x

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ModelingCoordinate

System

ImageCoordinate

System

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t

TextureCoordinate

System


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Texture Mapping When scan convert, map from

image coordinate system (x,y) tomodeling coordinate system (u,v) to

texture image (t,s)

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(1,1)(0,1)

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ModelingCoordinate

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Texture Mapping

Chris Buehler & Leonard McMillan, MIT

Texture mapping is a 2D projective transformationtexture coordinate system: (t,s) toimage coordinate system (x,y)

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Texture Mapping Scan conversion

Interpolate texture coordinates down/across scan linesDistortion due to bilinear interpolation approximation Cut polygons into smaller ones, or Perspective divide at each pixel

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Texture Mapping

Linear interpolationof texture coordinates

Correct interpolationwith perspective divide

Hill Figure 8.42

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Texture Filtering

Angel Figure 9.4

Must sample texture to determine colorat each pixel in image


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Texture Filtering

Angel Figure 9.5

Aliasing is a problem

Point sampling Area filtering

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Texture Mapping Scan conversion

Interpolate texture coordinates down/across scan linesDistortion due to bilinear interpolation approximation

Cut polygons into smaller ones, or Perspective divide at each pixel

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Texture Mapping

Linear interpolationof texture coordinates

Correct interpolationwith perspective divide

Hill Figure 8.42 T h o m a s

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Texture mapping applicationsModulation texturesIllumination mappingBump mappingEnvironment mapping

Image-based renderingNon-photorealistic rendering

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Texture Filtering

Angel Figure 9.4

Must sample texture to determine colorat each pixel in image

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Texture Filtering

Angel Figure 9.5

Aliasing is a problem

Point sampling Area filtering


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Texture Filtering Ideally, use elliptically shaped convolution fil ters

In practice, use rectangles T h o m a s

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Texture Filtering

Angel Figure 9.14

Size of fil ter depends on projective warpCan prefiltering images Mip maps

Summed area tables

Magnification Minification

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Mip Maps Keep textures prefiltered at multiple resolutions

For each pixel, linearly interpolate betweentwo closest levels (e.g., trilinear filtering)Fast, easy for hardware

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Summed-area tables At each texel keep sum of all values down&right

To compute sum of all values within a rectangle simplysubtract two entriesBetter ability to capture very oblique projectionsBut, cannot store values in a single byte

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Modulation textures

)))()(((),( S S T T L L Ln

S D A A E I K I K I S RV K L N K I K I t sT I

Map texture values to scale factor

W o o

d t e x

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Texturevalue

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Illumination Mapping

S S T T L L L

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S D A A E I K I K I S RV K L N K I K I I ))()((

Map texture values to surface material parameterKAKD

KSKTn

K T = T(s,t)

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Bump Mapping Map texture values to perturbations of surface

normals

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Bump Mapping

H&B Figure 14.100

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Environment Mapping Map texture values to perturbations of surface

normals

H&B Figure 14.93 T h o m a s

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Image-Based Rendering Map photographic textures to provide details for

coarsely detailed polygonal model


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Solid Textures Texture values indexed by 3D location

Expensive storage, orCompute on the fly, E.g Perlin noise

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Solid Textures Texture values indexed by 3D location

Expensive storage, orCompute on the fly, E.g Perlin noise

06b rendering iii

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