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CSCI480/582 Lecture 11 Chap.2.4 Orientation Along Path and Deformation Feb, 16, 2009

CSCI480/582 Lecture 11 Chap.2.4 Orientation Along Path and Deformation Feb, 16, 2009. Outline. Orientation along a path Free-form deformation. Representing orientations by Euler Angles. Euler angles using the z-x-z convention:. Gimbal Lock example.

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CSCI480/582 Lecture 11 Chap.2.4 Orientation Along Path and Deformation Feb, 16, 2009

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  1. CSCI480/582 Lecture 11 Chap.2.4 Orientation Along Path and Deformation Feb, 16, 2009

  2. Outline • Orientation along a path • Free-form deformation

  3. Representing orientations by Euler Angles Euler angles using the z-x-z convention: Gimbal Lock example

  4. Representing orientations by Quarternion A general Quaternion A Quaternion that can represent a rotation in 3D space The 4 elements can be further decomposed to [x0,y0,z0]

  5. Rotation Interpolation using Qurternion Given the begin rotation q1 and ending rotation q2, the interpolation function that gives the orientation in between is called spherical linear interpolation (slerp)

  6. 3D Object Deformation • Interpolation problems in 3-D parameter space: • Temporal: Given the beginning and ending shapes of an object, get the deformation function that produce the shapes in between the two boundary shapes • Spatial: Given the control points, interpolate a 3D volume inside the control points. • In contrast to • curve interpolation in 1-D parameter space, • or surface interpolation in 2-D parameter space • The same basis functions still apply to object deformation with increased amount of integrations.

  7. Free-form Deformation using Bezier Basis • Free-form refers to a grid of control points that are free to move in 3D space. • If Bezier basis function is chosen, then • Geometry interpolation from control points to object volume • Temporal change is then defined by changing the control points directly

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