Animating rotation with quaternion curves
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Visualizing Quaternions (The Morgan Kaufmann Series in Interactive 3D Technology)
Visualizing Quaternions (The Morgan Kaufmann Series in Interactive 3D Technology)
An Integrated Introduction to Computer Graphics and Geometric Modeling
An Integrated Introduction to Computer Graphics and Geometric Modeling
Graphical Models
| Hi-index | 0.00 |
We show how to represent perspective projections in 3-dimensions using rotations in 4-dimensions. This representation permits us to replace classical singular 4x4 matrices for perspective projection with nonsingular 4x4 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 4x4 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.