CMSC 635 Volume Rendering Volume data 3 D
![CMSC 635 Volume Rendering CMSC 635 Volume Rendering](https://slidetodoc.com/presentation_image_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/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_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/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_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/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_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/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_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/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_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/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_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/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_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/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_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/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_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/image-10.jpg)
![Appearance § Additive / pseudo-XRay § Volume lighting: , § Directional derivative Appearance § Additive / pseudo-XRay § Volume lighting: , § Directional derivative](https://slidetodoc.com/presentation_image_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/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_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/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_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/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_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/image-14.jpg)
![Shear-warp [Lacroute 94] Shear-warp [Lacroute 94]](https://slidetodoc.com/presentation_image_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/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_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/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_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/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_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/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_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/image-19.jpg)
- Slides: 19
![CMSC 635 Volume Rendering CMSC 635 Volume Rendering](https://slidetodoc.com/presentation_image_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/image-1.jpg)
CMSC 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_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/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_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/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_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/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_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/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_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/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_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/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_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/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_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/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_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/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_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/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_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/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_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/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_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/image-14.jpg)
Splatting [Westover 90] § Resample directly onto screen § Each voxel contributes kernel footprint § Accumulate back-to-front
![Shearwarp Lacroute 94 Shear-warp [Lacroute 94]](https://slidetodoc.com/presentation_image_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/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_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/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_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/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_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/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_h2/44b49c09bb8b1e131fd5f0f46d1f1d7d/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
Bulan arab
Ngr 635-100
Orea fintrac form
Ba 635
Ba 635
635 project
Jerry tessendorf
Introduction to volume rendering
Indirect volume rendering
Direct volume rendering ray casting
Vtk volume rendering c++ example
Berlatih teknik arsir gradasi dapat dimulai dengan membuat
Surfels: surface elements as rendering primitives
Rendering pipeline
Masaki kawase
Rendering pipeline in computer graphics
Christopher buehler
Reyes rendering
Photorealistic rendering carlsbad
Clustered forward rendering