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8.1si31_2001 SI31 Advanced Computer Graphics AGR Lecture 8 Polygon Rendering

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8.2si31_2001 The Story So Far n 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) set of facets n Next step: rendering a set of facets

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8.3si31_2001 First a Word on Normals n A polygon has two normals If the polygon is part of a solid object, one normal will face out, one will face in. We need to have a way of distinguishing them.

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8.4si31_2001 Surface Normals insideoutside, single normal n Each polygon facet is considered to have an inside and an outside, and a single normal n This is determined by the order in which vertices of facet are specified: – look at object from outside anti- clockwise – if polygon vertices are specified in anti- clockwise order, then normal points from inside to outside P1 P4 P3 P2

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8.5si31_2001 Rendering Polygons n We are now ready to consider rendering a set of polygon facets visible n For efficiency, we only want to render those that are visible to the camera

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8.6si31_2001 Back Face Culling polyhedron back-facing n If the facets belong to a solid object (a polyhedron) we do not need to render back-facing polygons Here only three facets need to be drawn - those that face towards the camera

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8.7si31_2001 Back Face Culling n 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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8.8si31_2001 Back Face Culling n It is efficient to carry this out in the viewing co-ordinate system – camera on z-axis pointing in negative z- direction – so V = (0,0,-1) n Thus the V.N>0 test becomes a test only on z-component of normal vector N z < 0 – ie test if z-component of normal points in negative z-direction

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8.9si31_2001 Back Face Culling n Back face culling is an extremely important efficiency gain in rendering and is typically the first step in visibility processing n We are left with a set of front facing polygons...

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8.10si31_2001 The Next Problem visible n Some facets will be obscured by others - we only want to draw (ie shade) the visible polygons

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8.11si31_2001 Solution - Z Buffer Algorithm n 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 want to draw the polygon nearest the camera, ie largest z 0 1 camera

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8.12si31_2001 Z Buffer Algorithm n We require two buffers: – frame buffer – frame buffer to hold colour of each pixel (in terms of RGB)... typically 24 bits – z-buffer – z-buffer to hold depth information for each pixel... typically 32 bits n Initialize: – frame buffer to the background colour of the scene colour (x,y) = (I RED, I GREEN, I BLUE ) background – z-buffer to zero (back clipping plane) depth (x,y) = 0

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8.13si31_2001 Z Buffer Algorithm n 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) = (I RED, I GREEN, I BLUE ) gouraud/phong n After all polygons processed, depth buffer contains depth of visible surfaces, and frame buffer the colour of these surfaces

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8.14si31_2001 Z Buffer - Strengths and Weaknesses n A major advantage of the z-buffer algorithm is its simplicity n A weakness (of now decreasing importance) is the amount of memory required n Limited precision for depth calculations in complex scenes (perspective effect again a problem)

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8.15si31_2001 Transparency n Polygons in practice may be opaque or semi-transparent – in OpenGL =1 represents opaque n Simple rendering: – render opaque polygons first, generating colour (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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8.16si31_2001 Better Transparency n Better results by storing for each pixel the depth and transparency of each surface n Surfaces can then be composited back to front in order to give more accurate images

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8.17si31_2001 Shadows n Z buffers also give us a nice way of doing shadows n The z buffer is a way of determining what is visible to the camera n For shadows, we need a way of determining what is visible to the light source

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8.18si31_2001 Shadow Z Buffer n We require a second z-buffer, called a shadow z-buffer n 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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8.19si31_2001 Shadow Z Buffer n To determine if point is in shadow: – take its position (x O, y O, z O ) in the camera view, and transform it into the corresponding position (x O, y O, z O ) in the light source view – look up the z value, say z L, in the shadow z-buffer at the position (x O, y O ) – if z L is closer to the light than z O, 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

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