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Saito, T. and Takahashi, T. Comprehensible Rendering of 3-D Shapes Proc. of SIGGRAPH '90 Genesis of Image Space NPR

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Operations on G-buffers to extract certain properties various images Combine these images with rendered images Image space algorithms Saito, T. and Takahashi, T. Comprehensible Rendering of 3-D Shapes Proc. of SIGGRAPH '90 G-buffers ?

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Computer-Generated Images Special kind of recording equipment yields special images x-ray images thermal images sonar images

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G-buffers Translate this approach to computer graphics Render algorithms to create images that show scene properties normally hidden to the viewer object ID distance to view plane surface normal patch coordinates (u,v) for spline surfaces … G-buffers (geometric buffers)

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Pixel color now encodes 3D information and not just illuminationPixel color now encodes 3D information and not just illumination Reveal information about the underlying geometryReveal information about the underlying geometry Operations on G-buffersOperations on G-buffers combinationcombination edge detectionedge detection … G-buffers

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eveal RGB-buffer

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eveal Object ID-buffer

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eveal Depth-buffer

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eveal Normal-buffer

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eveal RGB-buffer

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eveal Object ID-buffer

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eveal Depth-buffer

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eveal Normal-buffer

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Process pixel (x,y)

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Saito, T. and Takahashi, T. Comprehensible Rendering of 3-D Shapes Proc. of SIGGRAPH '90 Data structures + algorithms: Drawing discontinuities, edges, contour lines, curved hatching from the image buffer Edge classification : Profile - - the border line of an object on the screen Internal - - a line where two faces meet. Images generated: 1.Depth 2.First-order differential 3.Second-order differential 4.Profile 5.Internal edge

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Depth Image Distance: viewpoint to screenDepth of object (eye coordinate) One pixel length (eye coordinate) Grayscale image that maps [ d min, d max ] to [0, 255] Shaded image Depth image OpenGL depth image content extracted by glReadPixels with GL_DEPTH_COMPONENT Equalizes the gradient value of depth image with the slope of the surface.

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Depth Image Grayscale image that maps [ d min, d max ] to [0, 255]

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Depth image First-order differential Sobel’s filter Second-order differential

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Profile image Internal edge image Normalization of images Distinguishes discontinuities from continuous changes Limit of the gradient for the elimination of 0 th order discontinuities

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OID (Object ID) Image

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Operations on G-buffers (so far…) Edge detection RGB-buffer discontinuities in brightness (illumination), i.e., shadows, material, objects z-buffer discontinuities in depth, i.e. Object boundaries, also boundaries within one object (creases) OID-buffer discontinuities in “objects”, i.e., object silhouettes

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Schofield, S.. Non-photorealistic Rendering: A critical examination and proposed system PhD thesis, School of Art and Design, Middlesex University, May 1994 http://www.microgds.com/index.shtml

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We can augment the silhouette edges computed with the depth map by using surface normals as well. We will do this by using a normal map, which is an image that represents the surface normal at each point on an object. The values in each of the (R; G;B) color components of a point on the normal map correspond to the (x; y; z) surface normal at that point. Depth map Normal map Decaudin, P. Cartoon-looking rendering of 3d-scenes. Research Report #2919, INRIA Rocquencourt 1996. Using Normal Maps to Find Creases and Boundaries

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To compute the normal map for an object with a graphics package: First, we set the object color to white, and the material property to diffuse reflection. We then place a red light on the X axis, a green light on the Y axis, and a blue light on the Z axis, all facing the object. Additionally, we put lights with negative intensity on the opposite side of each axis. We then render the scene to produce the normal map. Each light will illuminate a point on the object in proportion to the dot product of the surface normal with the light’s axis. An example is shown in Figure (c,d). We can then detect edges in the normal map. These edges detect changes in surface orientation, and can be combined with the edges of the depth map to produce a reasonably good silhouette image (Figure (e)).

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Outline drawing with image processing. (a) Depth map. (b) Edges of the depth map. (c) Normal map. (d) Edges of the normal map. (e) The combined edge images.

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Outline detection of a more complex model. (a) Depth map. (b) Depth map edges. (c) Normal map. (d) Normal map edges. (e) Combined depth and normal map edges.

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Creates visible silhouette edges with constant thickness at the same depth value as the corresponding polygon edge Works well when dihedral angle between the adjacent front- and back- facing is not large As the line width increase, gaps may occur between silhouette edges Rossignac, J. and van Emmerik, M. Hidden contours on a frame-buffer Proc. of the 7th Eurographics Workshop on Computer Graphics Hardware, 1992.

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1.Fill background with white 2.Enable back-face culling, set depth function to “Less Than”” 3.Render front-face polygons in white 4.Enable front-face culling, set depth function to “Less Than or Equal To” 5.In black, draw back-facing polygons in wire-frame mode. 6.Repeat for a new viewpoint Rossignac, J. and van Emmerik, M. Hidden contours on a frame-buffer Proc. of the 7th Eurographics Workshop on Computer Graphics Hardware, 1992.

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