# lec9 - 3D orientation Computer Graphics Lecture 08 Contents...

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3D orientation Computer Graphics Lecture 08

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Contents Motivation Reminder – Rotation matrix Fixed Angle and Euler Angle Axis Angle Quaternion Summary
Motivation Joints and rotations Rotational DOFs are widely used in character animation 3 translational DOFs 48 rotational DOFs Each joint can have up to 3 DOFs 1 DOF: knee 2 DOF: wrist 3 DOF: arm

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Motivation cont’ Computer – Human interaction Virtual trackball
Reminder Rotation matrix Homogeneous coordinates (review) 4X4 matrix used to represent translation, scaling, and rotation a point in the space is represented as Treat all transformations the same so that they can be easily combined We talked about: Translation, Rotation and Scale matrices

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Reminder cont’ Composite transformations A series of transformations on an object can be applied as a series of matrix multiplications : position in the global coordinate : position in the local coordinate
Interpolation In order to “move things”, we need both translation and rotation Interpolating the translation is easy, but what about rotations?

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The problem Finding the most natural and compact way to present rotation and orientations Orientation interpolation which result in a natural motion A closed mathematical form that deals with rotation and orientations (expansion for the complex numbers)
Angles used to rotate about fixed axes Orientations are specified by a set of 3 ordered parameters that represent 3 ordered rotations about fixed axes, ie. first about x, then y, then z

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lec9 - 3D orientation Computer Graphics Lecture 08 Contents...

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