### Abstract

One of the most popular mathematical tools in fields of robotics, mechanisms and computer graphics is the 4×4 homogeneous transformation matrix. In previous work we applied this matrix to the optical domains of flat and spherical surfaces for: (1) skew ray tracing to determine the paths of skew rays being reflected/refracted; (2) sensitivity analysis to determine by direct mathematical analysis the differential change of incident point and reflected/refracted vector with respect to change in incident light source. The present work extends our previous work to include the case of parabaloidal boundary surfaces.

Original language | English |
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Title of host publication | Progress on Advanced Manufacture for Micro/Nano Technology 2005 - Proceedings of the 2005 International Conference on Advanced Manufacture |

Pages | 613-618 |

Number of pages | 6 |

Volume | 505-507 |

Edition | PART 1 |

Publication status | Published - 2006 |

Event | 2005 International Conference on Advanced Manufacture, ICAM2005 - Taipei, R.O.C., Taiwan Duration: 2005 Nov 28 → 2005 Dec 2 |

### Publication series

Name | Materials Science Forum |
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Number | PART 1 |

Volume | 505-507 |

ISSN (Print) | 0255-5476 |

### Other

Other | 2005 International Conference on Advanced Manufacture, ICAM2005 |
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Country | Taiwan |

City | Taipei, R.O.C. |

Period | 05-11-28 → 05-12-02 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Materials Science(all)

### Cite this

*Progress on Advanced Manufacture for Micro/Nano Technology 2005 - Proceedings of the 2005 International Conference on Advanced Manufacture*(PART 1 ed., Vol. 505-507, pp. 613-618). (Materials Science Forum; Vol. 505-507, No. PART 1).

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*Progress on Advanced Manufacture for Micro/Nano Technology 2005 - Proceedings of the 2005 International Conference on Advanced Manufacture.*PART 1 edn, vol. 505-507, Materials Science Forum, no. PART 1, vol. 505-507, pp. 613-618, 2005 International Conference on Advanced Manufacture, ICAM2005, Taipei, R.O.C., Taiwan, 05-11-28.

**Skew ray tracing and sensitivity analysis of paraboloidal optical boundary surfaces.** / Sung, Chi Kuen; Lin, Psang-Dain.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Skew ray tracing and sensitivity analysis of paraboloidal optical boundary surfaces

AU - Sung, Chi Kuen

AU - Lin, Psang-Dain

PY - 2006

Y1 - 2006

N2 - One of the most popular mathematical tools in fields of robotics, mechanisms and computer graphics is the 4×4 homogeneous transformation matrix. In previous work we applied this matrix to the optical domains of flat and spherical surfaces for: (1) skew ray tracing to determine the paths of skew rays being reflected/refracted; (2) sensitivity analysis to determine by direct mathematical analysis the differential change of incident point and reflected/refracted vector with respect to change in incident light source. The present work extends our previous work to include the case of parabaloidal boundary surfaces.

AB - One of the most popular mathematical tools in fields of robotics, mechanisms and computer graphics is the 4×4 homogeneous transformation matrix. In previous work we applied this matrix to the optical domains of flat and spherical surfaces for: (1) skew ray tracing to determine the paths of skew rays being reflected/refracted; (2) sensitivity analysis to determine by direct mathematical analysis the differential change of incident point and reflected/refracted vector with respect to change in incident light source. The present work extends our previous work to include the case of parabaloidal boundary surfaces.

UR - http://www.scopus.com/inward/record.url?scp=35348870417&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35348870417&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:35348870417

SN - 0878499903

SN - 9780878499908

VL - 505-507

T3 - Materials Science Forum

SP - 613

EP - 618

BT - Progress on Advanced Manufacture for Micro/Nano Technology 2005 - Proceedings of the 2005 International Conference on Advanced Manufacture

ER -