Vector field-based deformation
- Smooth vector field (or velocity) \(u:(x,y,z) \to (u_x(x,y,z),u_y(x,y,z),u_z(x,y,z))\)
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- At arbitrary time \(t\), \(\dot{p}(t)=u(p(t))\)
- Applying deformation = integrate vertex position along streamlines
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- \(\displaystyle p_1=p_0+\int_t u(p(t))\,\mathrm{d}t\)
- At a given time \(t\), the instantaneous deformation at position \(p\) is
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- \(f(p,t) = p + u(p,t) \rightarrow f=I+u\)
- (+) If \(\|u\|\neq 0\) (and \(\neq\) singularity) no-intersection
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- Streamlines do not intersect
- (-) Arbitrary vector fields hard to define and control.
- Note: All physically-based deformation can be seen as vector field deformations
