Spatial / Surface based deformation

• Consider a shape defined as \((p_i)_{i\in[0,N-1]}\) positions

Spatial/volume deformation

• Define spatial deformation \(\forall p\in\mathbb{R}^3\,,\;\;f: p \to f(p)\)
• • Apply \(f\) to every positions
  • \(\forall i\in[0,N-1]\,,\; q_i = f(p_i)\)

• (+) Independant from shape representation
• • Point sets, Surface, Volume.
• (-) Indirect control
• • Spatial deformation \(\to\) shape deformation
• (-) Deformation fully defined by spatial position

Surface-based

• Compute deformation on surface only
• • Deformation is defined at \(p_i\)
  • But not at arbitrary position in space

• • • ex. \(q_i = p_i+n_i\), \(\;\;n_i\):surface normal at position \(p_i\)

• (+) Can integrate/preserve surface properties (neighborood, curvature, etc.)
• (-) Sensible to surface representation & connectivity.