### Abstract

Projection methods for volume rendering unstructured data work by projecting, in visibility order, the polyhedral cells of the mesh onto the image plane, and incrementally compositing each cell's color and opacity into the final image. Normally, such methods require an algorithm to determine a visibility order of the cells. The Meshed Polyhedra Visibility Order (MPVO) algorithm can provide such an order for convex meshes by considering the implications of local ordering relations between cells sharing a common face. However, in nonconvex meshes, one must also consider ordering relations along viewing rays which cross empty space between cells. In order to include these relations, the algorithm described in this paper, the scanning exact meshed polyhedra visibility ordering (SXMPVO) algorithm, scan-converts the exterior faces of the mesh and saves the ray-face intersections in an A-Buffer data structure which is then used for retrieving the extra ordering relations. The image which SXMPVO produces is the same as would be produced by ordering the cells exactly, even though SXMPVO does not compute an exact visibility ordering. This is because the image resolution used for computing the visibility ordering relations is the same as that which is used for the actual volume rendering and we choose our A-Buffer rays at the same sample points that are used to establish a polygon's pixel coverage during hardware scan conversion. Thus, the algorithm is image-space correct. The SXMPVO algorithm has several desirable features; among them are speed, simplicity of implementation, and no extra (i.e., with respect to MPVO) preprocessing.

Original language | English (US) |
---|---|

Pages (from-to) | 695-707 |

Number of pages | 13 |

Journal | IEEE Transactions on Visualization and Computer Graphics |

Volume | 10 |

Issue number | 6 |

DOIs | |

State | Published - Nov 2004 |

### Fingerprint

### Keywords

- Unstructured mesh
- Visibility ordering
- Volume rendering

### ASJC Scopus subject areas

- Computer Graphics and Computer-Aided Design
- Software

### Cite this

*IEEE Transactions on Visualization and Computer Graphics*,

*10*(6), 695-707. https://doi.org/10.1109/TVCG.2004.45

**Image-space visibility ordering for cell projection volume rendering of unstructured data.** / Cook, Richard; Max, Nelson; Silva, Cláudio T.; Williams, Peter L.

Research output: Contribution to journal › Article

*IEEE Transactions on Visualization and Computer Graphics*, vol. 10, no. 6, pp. 695-707. https://doi.org/10.1109/TVCG.2004.45

}

TY - JOUR

T1 - Image-space visibility ordering for cell projection volume rendering of unstructured data

AU - Cook, Richard

AU - Max, Nelson

AU - Silva, Cláudio T.

AU - Williams, Peter L.

PY - 2004/11

Y1 - 2004/11

N2 - Projection methods for volume rendering unstructured data work by projecting, in visibility order, the polyhedral cells of the mesh onto the image plane, and incrementally compositing each cell's color and opacity into the final image. Normally, such methods require an algorithm to determine a visibility order of the cells. The Meshed Polyhedra Visibility Order (MPVO) algorithm can provide such an order for convex meshes by considering the implications of local ordering relations between cells sharing a common face. However, in nonconvex meshes, one must also consider ordering relations along viewing rays which cross empty space between cells. In order to include these relations, the algorithm described in this paper, the scanning exact meshed polyhedra visibility ordering (SXMPVO) algorithm, scan-converts the exterior faces of the mesh and saves the ray-face intersections in an A-Buffer data structure which is then used for retrieving the extra ordering relations. The image which SXMPVO produces is the same as would be produced by ordering the cells exactly, even though SXMPVO does not compute an exact visibility ordering. This is because the image resolution used for computing the visibility ordering relations is the same as that which is used for the actual volume rendering and we choose our A-Buffer rays at the same sample points that are used to establish a polygon's pixel coverage during hardware scan conversion. Thus, the algorithm is image-space correct. The SXMPVO algorithm has several desirable features; among them are speed, simplicity of implementation, and no extra (i.e., with respect to MPVO) preprocessing.

AB - Projection methods for volume rendering unstructured data work by projecting, in visibility order, the polyhedral cells of the mesh onto the image plane, and incrementally compositing each cell's color and opacity into the final image. Normally, such methods require an algorithm to determine a visibility order of the cells. The Meshed Polyhedra Visibility Order (MPVO) algorithm can provide such an order for convex meshes by considering the implications of local ordering relations between cells sharing a common face. However, in nonconvex meshes, one must also consider ordering relations along viewing rays which cross empty space between cells. In order to include these relations, the algorithm described in this paper, the scanning exact meshed polyhedra visibility ordering (SXMPVO) algorithm, scan-converts the exterior faces of the mesh and saves the ray-face intersections in an A-Buffer data structure which is then used for retrieving the extra ordering relations. The image which SXMPVO produces is the same as would be produced by ordering the cells exactly, even though SXMPVO does not compute an exact visibility ordering. This is because the image resolution used for computing the visibility ordering relations is the same as that which is used for the actual volume rendering and we choose our A-Buffer rays at the same sample points that are used to establish a polygon's pixel coverage during hardware scan conversion. Thus, the algorithm is image-space correct. The SXMPVO algorithm has several desirable features; among them are speed, simplicity of implementation, and no extra (i.e., with respect to MPVO) preprocessing.

KW - Unstructured mesh

KW - Visibility ordering

KW - Volume rendering

UR - http://www.scopus.com/inward/record.url?scp=29244440771&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=29244440771&partnerID=8YFLogxK

U2 - 10.1109/TVCG.2004.45

DO - 10.1109/TVCG.2004.45

M3 - Article

C2 - 15527051

AN - SCOPUS:29244440771

VL - 10

SP - 695

EP - 707

JO - IEEE Transactions on Visualization and Computer Graphics

JF - IEEE Transactions on Visualization and Computer Graphics

SN - 1077-2626

IS - 6

ER -