An Inexpensive Bounding Representation for Offsets of Quadratic Curves
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We describe a simple mechanism for bounding the portion of the plane lying between a quadratic Beizer curve segment and its offset curve at distance d. Instead of comprising one or more partial bounding polygons, our representation consists of only a single approximate offset curve segment, also in quadratic Bezier form. Evaluated on a corpus of real-world curves, this technique avoids 68-99% of antialias-distance queries and 41-96% of brushparameter queries. A proof of correctness is provided.
BibTeX
@inproceedings {10.1145:2018323.2018346,
booktitle = {Eurographics/ ACM SIGGRAPH Symposium on High Performance Graphics},
editor = {Carsten Dachsbacher and William Mark and Jacopo Pantaleoni},
title = {{An Inexpensive Bounding Representation for Offsets of Quadratic Curves}},
author = {Ruf, Erik},
year = {2011},
publisher = {ACM},
ISSN = {2079-8687},
ISBN = {978-1-4503-0896-0},
DOI = {10.1145/2018323.2018346}
}
booktitle = {Eurographics/ ACM SIGGRAPH Symposium on High Performance Graphics},
editor = {Carsten Dachsbacher and William Mark and Jacopo Pantaleoni},
title = {{An Inexpensive Bounding Representation for Offsets of Quadratic Curves}},
author = {Ruf, Erik},
year = {2011},
publisher = {ACM},
ISSN = {2079-8687},
ISBN = {978-1-4503-0896-0},
DOI = {10.1145/2018323.2018346}
}