کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
442453 | 692249 | 2013 | 15 صفحه PDF | دانلود رایگان |
We show how to represent perspective projections in 3-dimensions using rotations in 4-dimensions. This representation permits us to replace classical singular 4 × 4 matrices for perspective projection with nonsingular 4 × 4 orthogonal matrices. This approach also allows us to compute perspective projections by sandwiching vectors between two copies of a unit quaternion. In addition to deriving explicit formulas for these 4 × 4 rotation matrices for perspective projection, we also explain the geometric intuition underlying the observation that perspective projections in 3-dimensions can be represented by rotations in 4-dimensions. We show too that every rotation in 4-dimensions models either a rotation, a reflection, a perspective projection, or one of their composites in 3-dimensions.
Figure optionsDownload as PowerPoint slideHighlights
► How to represent perspective projections in 3-dimensions using rotations in 4-dimensions.
► How to replace classical singular 4 × 4 matrices for perspective projection with nonsingular 4 × 4 orthogonal matrices.
► How to compute perspective projections by sandwiching vectors between two copies of a unit quaternion.
Journal: Graphical Models - Volume 75, Issue 2, March 2013, Pages 41–55