CMSC 491635 Volume Rendering Volume data 3 D
![CMSC 491/635 Volume Rendering CMSC 491/635 Volume Rendering](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-1.jpg)
![Volume data § 3 D Scalar Field: F(x, y, z) = ? Implicit functions Volume data § 3 D Scalar Field: F(x, y, z) = ? Implicit functions](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-2.jpg)
![Implicit functions § Blobs [Blinn 82] § Metaballs [Nishimura 83] § Soft Objects [Wyvill Implicit functions § Blobs [Blinn 82] § Metaballs [Nishimura 83] § Soft Objects [Wyvill](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-3.jpg)
![Voxels § Sampled volume Usually in a grid § Measured MRI, CT scan, … Voxels § Sampled volume Usually in a grid § Measured MRI, CT scan, …](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-4.jpg)
![Isosurface rendering § § F(x, y, z) – c = 0 (for some given Isosurface rendering § § F(x, y, z) – c = 0 (for some given](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-5.jpg)
![Marching cubes § Estimate intersection point on each edge Same criteria (e. g. linear Marching cubes § Estimate intersection point on each edge Same criteria (e. g. linear](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-6.jpg)
![Marching tetrahedra § Decompose volume into tetrahedra § Avoids ambiguous “opposite corner” cases § Marching tetrahedra § Decompose volume into tetrahedra § Avoids ambiguous “opposite corner” cases §](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-7.jpg)
![Direct volume rendering § Model as translucent material Color and extinction Attenuation along ray Direct volume rendering § Model as translucent material Color and extinction Attenuation along ray](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-8.jpg)
![Simplify volume integral § Numeric integration, step size d Color of ray segment § Simplify volume integral § Numeric integration, step size d Color of ray segment §](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-9.jpg)
![Transfer functions Map scalar to color and/or opacity Transfer functions Map scalar to color and/or opacity](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-10.jpg)
![Appearance § Additive / pseudo-XRay § Volume lighting: , § Directional derivative Appearance § Additive / pseudo-XRay § Volume lighting: , § Directional derivative](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-11.jpg)
![Rendering methods § § § Ray casting Splatting Texture accumulation Shear-warp Fourier volume rendering Rendering methods § § § Ray casting Splatting Texture accumulation Shear-warp Fourier volume rendering](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-12.jpg)
![Ray casting § § § Straightforward numerical integration Uniform steps along ray Resample volume Ray casting § § § Straightforward numerical integration Uniform steps along ray Resample volume](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-13.jpg)
![Splatting [Westover 90] § Resample directly onto screen § Each voxel contributes kernel footprint Splatting [Westover 90] § Resample directly onto screen § Each voxel contributes kernel footprint](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-14.jpg)
![Shear-warp [Lacroute 94] Shear-warp [Lacroute 94]](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-15.jpg)
![Texture accumulation § § § Let texturing hardware resample Accumulate back-to-front 3 D textures Texture accumulation § § § Let texturing hardware resample Accumulate back-to-front 3 D textures](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-16.jpg)
![Pre-integrated texture [Engel 01] § Improve approximation for and Lookup(start value, end value, d) Pre-integrated texture [Engel 01] § Improve approximation for and Lookup(start value, end value, d)](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-17.jpg)
![Pre-integrated texture § § a: shading before resampling b: shading after resampling c: b Pre-integrated texture § § a: shading before resampling b: shading after resampling c: b](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-18.jpg)
![Dividing cubes § § Find voxels that cross isosurface Subdivide to pixel-sized sub-voxels Find Dividing cubes § § Find voxels that cross isosurface Subdivide to pixel-sized sub-voxels Find](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-19.jpg)
- Slides: 19
![CMSC 491635 Volume Rendering CMSC 491/635 Volume Rendering](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-1.jpg)
CMSC 491/635 Volume Rendering
![Volume data 3 D Scalar Field Fx y z Implicit functions Volume data § 3 D Scalar Field: F(x, y, z) = ? Implicit functions](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-2.jpg)
Volume data § 3 D Scalar Field: F(x, y, z) = ? Implicit functions Voxel grid § Scalar data Density Temperature Wind speed …
![Implicit functions Blobs Blinn 82 Metaballs Nishimura 83 Soft Objects Wyvill Implicit functions § Blobs [Blinn 82] § Metaballs [Nishimura 83] § Soft Objects [Wyvill](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-3.jpg)
Implicit functions § Blobs [Blinn 82] § Metaballs [Nishimura 83] § Soft Objects [Wyvill 86] Polynomial approximation for exp() Philo Vivero http: //faemalia. org
![Voxels Sampled volume Usually in a grid Measured MRI CT scan Voxels § Sampled volume Usually in a grid § Measured MRI, CT scan, …](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-4.jpg)
Voxels § Sampled volume Usually in a grid § Measured MRI, CT scan, … § Computed Sample geometric model Finite element simulation …
![Isosurface rendering Fx y z c 0 for some given Isosurface rendering § § F(x, y, z) – c = 0 (for some given](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-5.jpg)
Isosurface rendering § § F(x, y, z) – c = 0 (for some given c) Isosurface normal: F Implicit: Point repulsion [Witkin 92] Voxel: Marching cubes [Lorensen 87]
![Marching cubes Estimate intersection point on each edge Same criteria e g linear Marching cubes § Estimate intersection point on each edge Same criteria (e. g. linear](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-6.jpg)
Marching cubes § Estimate intersection point on each edge Same criteria (e. g. linear interpolation) Polygons will match § Use template for polygons 28 possibilities, 15 “unique” Store templates in table
![Marching tetrahedra Decompose volume into tetrahedra Avoids ambiguous opposite corner cases Marching tetrahedra § Decompose volume into tetrahedra § Avoids ambiguous “opposite corner” cases §](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-7.jpg)
Marching tetrahedra § Decompose volume into tetrahedra § Avoids ambiguous “opposite corner” cases § 24 = 16 cases, 3 unique 0 or 4 points inside (0 triangles) 1 or 3 points inside (1 triangle) 2 points inside (2 triangles)
![Direct volume rendering Model as translucent material Color and extinction Attenuation along ray Direct volume rendering § Model as translucent material Color and extinction Attenuation along ray](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-8.jpg)
Direct volume rendering § Model as translucent material Color and extinction Attenuation along ray , § Attenuated color at § Accumulate attenuated colors along ray §
![Simplify volume integral Numeric integration step size d Color of ray segment Simplify volume integral § Numeric integration, step size d Color of ray segment §](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-9.jpg)
Simplify volume integral § Numeric integration, step size d Color of ray segment § Back to front composite
![Transfer functions Map scalar to color andor opacity Transfer functions Map scalar to color and/or opacity](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-10.jpg)
Transfer functions Map scalar to color and/or opacity
![Appearance Additive pseudoXRay Volume lighting Directional derivative Appearance § Additive / pseudo-XRay § Volume lighting: , § Directional derivative](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-11.jpg)
Appearance § Additive / pseudo-XRay § Volume lighting: , § Directional derivative
![Rendering methods Ray casting Splatting Texture accumulation Shearwarp Fourier volume rendering Rendering methods § § § Ray casting Splatting Texture accumulation Shear-warp Fourier volume rendering](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-12.jpg)
Rendering methods § § § Ray casting Splatting Texture accumulation Shear-warp Fourier volume rendering
![Ray casting Straightforward numerical integration Uniform steps along ray Resample volume Ray casting § § § Straightforward numerical integration Uniform steps along ray Resample volume](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-13.jpg)
Ray casting § § § Straightforward numerical integration Uniform steps along ray Resample volume to sample points Before classification and/or shading After classification and/or shading
![Splatting Westover 90 Resample directly onto screen Each voxel contributes kernel footprint Splatting [Westover 90] § Resample directly onto screen § Each voxel contributes kernel footprint](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-14.jpg)
Splatting [Westover 90] § Resample directly onto screen § Each voxel contributes kernel footprint Reconstruction + pixel filter § Accumulate back-to-front
![Shearwarp Lacroute 94 Shear-warp [Lacroute 94]](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-15.jpg)
Shear-warp [Lacroute 94]
![Texture accumulation Let texturing hardware resample Accumulate backtofront 3 D textures Texture accumulation § § § Let texturing hardware resample Accumulate back-to-front 3 D textures](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-16.jpg)
Texture accumulation § § § Let texturing hardware resample Accumulate back-to-front 3 D textures Render slices parallel to image plane Shift accesses for , § 2 D texture slices Slice sets perpendicular to each axis Choose set most parallel to image plane
![Preintegrated texture Engel 01 Improve approximation for and Lookupstart value end value d Pre-integrated texture [Engel 01] § Improve approximation for and Lookup(start value, end value, d)](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-17.jpg)
Pre-integrated texture [Engel 01] § Improve approximation for and Lookup(start value, end value, d) § Dependent lookup 3 D texture 2 D texture § linear in d § constant d
![Preintegrated texture a shading before resampling b shading after resampling c b Pre-integrated texture § § a: shading before resampling b: shading after resampling c: b](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-18.jpg)
Pre-integrated texture § § a: shading before resampling b: shading after resampling c: b with interpolated slices d: pre-integrated, same slice set as b
![Dividing cubes Find voxels that cross isosurface Subdivide to pixelsized subvoxels Find Dividing cubes § § Find voxels that cross isosurface Subdivide to pixel-sized sub-voxels Find](https://slidetodoc.com/presentation_image_h2/8fafdf8980caa7d114b8c217de86c019/image-19.jpg)
Dividing cubes § § Find voxels that cross isosurface Subdivide to pixel-sized sub-voxels Find sub-voxels that cross isosurface Plot as shaded points / kernel footprints
Jerry tessendorf
Introduction to volume rendering
Indirect volume rendering
Direct volume rendering ray casting
What is vtk
Teknik arsir bayangan
Blockinmax
Camera translate
High dynamic range rendering
Rendering pipeline in computer graphics
Unstructured lumigraph rendering
Reyes rendering
Photorealistic rendering carlsbad
Clustered shading
Shadow rendering techniques
"splat"
Car paint rendering
Windows color system
Light transport
Visual rendering