Saito, T. and Takahashi, T.Comprehensible Rendering of 3-D ShapesProc. of SIGGRAPH '90

Genesis of Genesis of Image Space NPRImage Space NPR

• 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 ShapesProc. of SIGGRAPH '90

G-buffers ?

Computer-Generated Images

Special kind of recording equipment yields special images

• x-ray images• thermal images• sonar images

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)

• PixelPixel color now encodes 3D information color now encodes 3D information and not just illuminationand not just illumination

• RReveal information about the underlyingeveal information about the underlying geometrygeometry

• OOperations on G-buffersperations on G-buffers• combinationcombination• edge detectionedge detection• ……

G-buffers

evealRGB-buffer

evealObject ID-buffer

evealDepth-buffer

evealNormal-buffer

evealRGB-buffer

evealObject ID-buffer

evealDepth-buffer

evealNormal-buffer

Process pixel (x,y)

Saito, T. and Takahashi, T.Comprehensible Rendering of 3-D ShapesProc. 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. Depth2. First-order differential3. Second-order differential4. Profile5. Internal edge

vs wz

dz

2

Depth Image

Distance: viewpoint to screen Depth of object(eye coordinate)

One pixel length(eye coordinate)

Grayscale image that maps [dmin, dmax] 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.

Depth ImageGrayscale image that maps [dmin, dmax] to [0, 255]

HGF

EXD

CBA

8

22

22

RDAHEC

HGFCBA

Xg

3

8 HGFEDCBAXXl

Depth image

First-order differential

Sobel’s filter

Second-order differential

p

gk

gg

gg

gg

min

minmax

min gkggif minmax

gkggif minmax

e

lkg

l

l

2max

lkggif minmax

lkgif max

Profile image

Internal edge image

Normalization of images

g

2lk

10gk

l

Distinguishes discontinuities from continuous changes

Limit of the gradient for the elimination of 0th order discontinuities

OID (Object ID) Image

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

Schofield, S..Non-photorealistic Rendering: A critical examination and proposed systemPhD thesis, School of Art and Design, Middlesex University, May 1994

http://www.microgds.com/index.shtml

We can augment the silhouette edgescomputed with the depth map by usingsurface 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 anobject.

The values in each of the (R; G;B) colorcomponents of a point on thenormal 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

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)).

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.

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.

• 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-bufferProc. of the 7th Eurographics Workshop on Computer Graphics Hardware, 1992.

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-bufferProc. of the 7th Eurographics Workshop on Computer Graphics Hardware, 1992.