[Course] An Elementary Introduction to Matrix Exponential for CG

Hiroyuki Ochiai, Ken Anjyo, Ayumi Kimura

SIGGRAPH '16 ACM SIGGRAPH 2016 Courses Article No. 4 (The movie and talk slides are available)

This course presents an elementary, intuitive, and visual introduction to several mathematical basics for beginners in computer graphics. The mathematical concepts covered in this course include 2D/3D translation, rotation, affine transformation, quaternion, dual quaternion, exponential and logarithm. These are quite useful for various aspects of computer graphics, including curve/surface editing, deformation and animation of geometric objects. On one hand we don't assume that the audience has familiarity with such mathematical concepts. Elements of linear algebra and calculus at undergraduate level are sufficient for the attendees of this course. To clarify the relation between these concepts and computer graphics practice, several graphics techniques will also be demonstrated, such as morphing (ARAP), cage-based deformation and Poisson mesh editing.

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