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GR2Advanced Computer

GraphicsAGR

GR2Advanced Computer

GraphicsAGR

Lecture 8Polygon Rendering

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The Story So FarThe Story So Far

We now understand:– how to model objects as a set of

polygonal facets and create a 3D world (Lectures 1 & 2)

– how to view these worlds with a camera model, projecting the facets to 2D (Lectures 3 & 4)

– how to calculate reflection off a surface (Lectures 5 & 6)

– how to shade a single projected facet using the reflection calculation (Lecture 7)

Next step: rendering a set of facetsset of facets

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First a Word on NormalsFirst a Word on Normals

A polygon has two normals

If the polygon is part of a solid object, one normal willface out, one will face in. We need to have a way ofdistinguishing them.

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Surface NormalsSurface Normals

Each polygon facet is considered to have an insideinside and an outside, outside, and a single normalsingle normal

This is determined by the order in which vertices of facet are specified:– look at object from outside– if polygon vertices are specified in

anti-clockwiseanti-clockwise order, then normal points from inside to outside

P1

P4

P3

P2

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Rendering PolygonsRendering Polygons

We are now ready to consider rendering a set of polygon facets

For efficiency, we only want to render those that are visiblevisible to the camera

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Back Face CullingBack Face Culling

If the facets belong to a solid object (a polyhedronpolyhedron) we do not need to render back-facingback-facing polygons

Here only threefacets need tobe drawn - thosethat face towardsthe camera

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Back Face CullingBack Face Culling

A polygon faces away from the viewer if the angle between the surface normal (N) and the viewing direction (V) is less than 90 degrees

V.N > 0

camera

V

N

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Back Face CullingBack Face Culling

It is efficient to carry this out in the viewing coordinate system– camera on z-axis pointing in negative z-

direction– so V = (0,0,-1)

Thus the V.N>0 test becomes a test only on z-component of normal vector

Nz < 0– ie test if z-component of normal points

in negative z-direction

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Back Face CullingBack Face Culling

Back face culling is an extremely important efficiency gain in rendering and is typically the first step in visibility processing

We are left with a set of front facing polygons...

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The Next ProblemThe Next Problem

Some facets will be obscured by others - we only want to draw (ie shade) the visiblevisible polygons

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Solution - Z Buffer Algorithm

Solution - Z Buffer Algorithm

Suppose polygons have been passed through the projection transformation, with the z-co-ordinate retained (ie the depth information) - suppose z normalized to range 0 to 1

z

x

y

view plane window

For each pixel(x,y), we wantto draw thepolygon nearestthe camera, ielargest z 0

1 camera

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Z Buffer AlgorithmZ Buffer Algorithm

We require two buffers:– frame buffer frame buffer to hold colour of each pixel

(in terms of RGB) ... typically 24 bits– z-bufferz-buffer to hold depth information for

each pixel ... typically 32 bits Initialize:

– frame buffer to the background colour of the scene

colour (x,y) = (IRED, IGREEN, IBLUE)background

– z-buffer to zero (back clipping plane)

depth (x,y) = 0

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Z Buffer AlgorithmZ Buffer Algorithm

As each polygon is scan converted and shaded using Gouraud or Phong shading:– calculate depth z for each pixel (x,y) in

polygon– if z > depth(x,y), then set:

depth (x,y) = z;

colour (x,y) = (IRED, IGREEN, IBLUE)gouraud/phong

After all polygons processed, depth buffer contains depth of visible surfaces, and frame buffer the colour of these surfaces

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Z Buffer - Strengths and Weaknesses

Z Buffer - Strengths and Weaknesses

A major advantage of the z-buffer algorithm is its simplicity

A weakness (of now decreasing importance) is the amount of memory required

Limited precision for depth calculations in complex scenes (perspective effect again a problem)

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TransparencyTransparency

Polygons in practice may be opaque or semi-transparent– in OpenGL =1 represents opaque

Simple rendering:– render opaque polygons first,

generatingcolour (x,y)

– for each semi-transparent polygon (with opacity , render into another buffer as

polygon (x,y)– and combine using:( 1 - ) * colour (x,y) + * polygon (x,y)

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Better TransparencyBetter Transparency

Better results by storing for each pixel the depth and transparency of each surface

Surfaces can then be composited back to front in order to give more accurate images

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ShadowsShadows

Z buffers also give us a nice way of doing shadows

The z buffer is a way of determining what is visible to the camera

For shadows, we need a way of determining what is visible to the light source

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Shadow Z BufferShadow Z Buffer

We require a second z-buffer, called a shadow z-buffer

Two step algorithm:– scene is ‘rendered’ from the light

source as viewpoint, with depth information stored in the shadow z-buffer (no need to calculate intensities)

– scene is rendered from the camera position, using Gouraud or Phong shading with a z-buffer algorithm ... but we need to adjust colour if point is in shadow

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Shadow Z BufferShadow Z Buffer

To determine if point is in shadow:– take its position (xO, yO, zO) in the camera

view, and transform it into the corresponding position (xO’, yO’, zO’) in the light source view

– look up the z value, say zL , in the shadow z-buffer at the position (xO’, yO’)

– if zL is closer to the light than zO’, this means some object is nearer the light and therefore the point is in shadow... in this case only the ambient reflection would be shown at that point