Understanding 3D Textures, Volume Rendering, and Applications, Study notes of Computer Science

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3D Textures and Volume Rendering

 3D texture objects



Samplers and access functions

 3D texture applications.

 Volume rendering (scalar field visualization)

3D Textures Objects

 Same OpenGL functions as 2D textures except...

 (^) Target = GL_TEXTURE_3D  (^) Upload texture image using glTexImage3D  (^) glTexImage3D(GL_TEXTURE_3D, 0, GL_RGB8, width, height, depth, 0, GL_RGB, GL_UNSIGNED_BYTE, pData);  (^) Assign 3D texture coordinates  (^) glTexCoord3f(s, t, r);

3D Texture Use

 Same principles as 2D textures

 (^) Yes, there is still mipmapping  (^) Yes, texture filtering still happens  (^) Yes, you can even render to 3D texture (one slice at a time)  (^) Single element of a 3D texture is referred to as a 'voxel', not a 'pixel'

 But be careful

 (^) 3D textures can be large  (^) Filtering is more expensive

3D texture applications

 “Solid textures” can give the appearance that an object

was carved out of a block of material.

Other uses

 Hold frames of animated texture

 (^) Third dimension is time 

High dimensional look-up tables

 (^) As used in factored lighting equations

 3D Light maps

Volume Rendering



The scalar field consists of :

 (^) emission colors: c(s(x))  (^) absorption colors : τ(s(x)) 

We will shoot rays x(t) through the eye, from the scalar

field and determine what color, C, the pixel in the viewing

plane should be.

ray: x(t) scalar field : s(x)

Volume Rendering

Evaluating the volume rendering integral:

 (^) Replace integrals with sums   (^) Replace ep+q^ with epeq^ in absorption term   (^) Write attenuation in terms of opacity variables 

٠ d

f dt ∑

٠ d f  t e ∑ i   xi   t

i e  xi  t e ∑ i   xi   t

i e  xi  t ١− Ai = e   xi   t

Volume Rendering

Evaluating the volume rendering integral:

 (^) Replace integrals with sums   (^) Does this look familiar?  (^) Looks like alpha blending

C =∑

i =٠ n

ci ∏

j =٠ i ١− A (^) j 

Volume Rendering Using Texture Slicing

 Useful blending functions

 (^) glBlendFunc(GL_ONE, GL_ONE_MINUS_SRC_ALPHA);  (^) “Over operator”  (^) glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);  (^) Maximum intensity projection “MIP”  (^) glBlendFunc(GL_ONE, GL_ONE)  (^) glBlendEquationEXT(GL_MAX_EXT)  (^) Best to render to floating point frame buffer for improved precision.

Problems

 Rendering too few slices leads to sampling artifacts.



View dependent sampling rate

Volume Rendering Implementation

 Approach 3 : View aligned slices

 (^) Enable alpha blending  (^) Set the texture matrix to the inverse of the view matrix  (^) or use OpenGL automatic texture coordinate generation  (^) Draw many quadrilaterals in eye space from back to front with the texture coordinates as shown 0,0,0 1,0, 0,1,0 1,1, 1,1, 1,0, 0,1,

View aligned slices



Sampling rate is always the same since the slices are not

rotating relative to the viewer

The transfer function

 Most volume data are scalar valued



The transfer function maps scalar values to colors



Only evaluate the transfer function at render time.

 Advantages over storing colors directly in 3D texture

 (^) Requires less storage space.  (^) Enables the transfer function to be interactively edited by the user without updating the whole 3D texture.

Using the transfer function

 Since rays don't always pass through voxel centers some

interpolation is necessary.



When does this interpolation happen relative to the

transfer function evaluation?

2 options:

 Preclassification

 (^) Assign colors to 3D voxel values by evaluating transfer func.  (^) Interpolate colors.

 Postclassification

 (^) Interpolate 3d voxel values  (^) Evaluate transfer function on interpolated value