Modeling Hair-Hair Interactions Using Sparse Guide Hairs Yizhou Yu Joint work with Johnny Chang and Jingyi Jin Department of Computer Science University of Illinois at Urbana-Champaign Yizhou Yu Joint work with Johnny Chang and Jingyi Jin Department of Computer Science University of Illinois at Urbana-Champaign

Dynamic Hair Interactions Hair-Hair Collision –Volumetric Appearance –Computationally Expensive for >50,000 Hairs Adhesive Forces due to Cosmetics, Interweaving, Static Charges –Hairstyle Recovery after Minor Movements Hairs are hard to stretch, and interactions become obvious when they are sufficiently close. Hair-Hair Collision –Volumetric Appearance –Computationally Expensive for >50,000 Hairs Adhesive Forces due to Cosmetics, Interweaving, Static Charges –Hairstyle Recovery after Minor Movements Hairs are hard to stretch, and interactions become obvious when they are sufficiently close.

Hair Simulation Using Sparse Guide Hairs Simulating Sparse Guide Hairs –Single strand dynamics for each guide hair –Simulating adhesive forces using static links –Simulating hair-hair collisions using density modulated triangle strips Dense Hair Simulation by Interpolation –Hair interpolation happens at each frame. –Fixed correspondences between dense hairs and guide hairs to achieve temporal coherence –Hair-object collisions are handled after interpolation for each individual strand. Simulating Sparse Guide Hairs –Single strand dynamics for each guide hair –Simulating adhesive forces using static links –Simulating hair-hair collisions using density modulated triangle strips Dense Hair Simulation by Interpolation –Hair interpolation happens at each frame. –Fixed correspondences between dense hairs and guide hairs to achieve temporal coherence –Hair-object collisions are handled after interpolation for each individual strand.

Guide Hair Modeling Modeling hair flows with vector fields

Video: Guide Hairs

Related Work on Hair Animation Single Strand Dynamics –Mass-Spring-Hinge Model [ Rosenblum et. al. 91 ], [ Daldegan et. al. 93 ] –Cantilever Beam [ Anjyo et. al. 92 ] –Multi-body Open Chain [ Hadap & Thalman 01 ] Hair-Hair Interactions –Fluid-based Model [ Hadap & Thalman 01 ] –Wisp-based Model [ Plante et. al. 01 ] Single Strand Dynamics –Mass-Spring-Hinge Model [ Rosenblum et. al. 91 ], [ Daldegan et. al. 93 ] –Cantilever Beam [ Anjyo et. al. 92 ] –Multi-body Open Chain [ Hadap & Thalman 01 ] Hair-Hair Interactions –Fluid-based Model [ Hadap & Thalman 01 ] –Wisp-based Model [ Plante et. al. 01 ]

Hair Strand Dynamics Each hair strand is modeled as a rigid multi- body open chain Forward Dynamics –Featherstone’s algorithm or Lagrange’s equations for generalized coordinates. Joint actuator force accounts for the bending and torsional rigidity of the strand. –Deviation from the resting position results in a nonzero resisting actuator force. Hair-hair interactions are formulated as external forces in addition to gravity. Each hair strand is modeled as a rigid multi- body open chain Forward Dynamics –Featherstone’s algorithm or Lagrange’s equations for generalized coordinates. Joint actuator force accounts for the bending and torsional rigidity of the strand. –Deviation from the resting position results in a nonzero resisting actuator force. Hair-hair interactions are formulated as external forces in addition to gravity.

Static Links Breakable Elastic Connections among Nearby Guide Hairs –Simulate the bonding effects formed when hair is in still –Enhance hairstyle recovery after minor movements. Static links enforce neighborhood configurations by exerting external forces onto the hair strands. Breakable Elastic Connections among Nearby Guide Hairs –Simulate the bonding effects formed when hair is in still –Enhance hairstyle recovery after minor movements. Static links enforce neighborhood configurations by exerting external forces onto the hair strands.

Static Links as Positional Springs Introduce a local coordinate system to each segment of the hair strands. Transform points on the nearby strands to the segment’s local system and keep them as the reference points. Forces are generated to recover the original relative positions of these reference points. Introduce a local coordinate system to each segment of the hair strands. Transform points on the nearby strands to the segment’s local system and keep them as the reference points. Forces are generated to recover the original relative positions of these reference points.

Force from Static Links The accumulated force a segment receives due to static links can be formulated as –ks is the spring constant kd is the damping constant, v is the time derivative of l, and A static link can be broken when its length change exceeds a threshold. The accumulated force a segment receives due to static links can be formulated as –ks is the spring constant kd is the damping constant, v is the time derivative of l, and A static link can be broken when its length change exceeds a threshold.

Dynamic Interactions Use of auxiliary triangle strips to imagine the space in between the set of sparse guide hair Collisions between the hair segments and the triangle strips are explicitly considered Use of auxiliary triangle strips to imagine the space in between the set of sparse guide hair Collisions between the hair segments and the triangle strips are explicitly considered

Modeling Hair Density Every face on a triangle strip is associated with a density value which can be zero. –The length of the triangle edges serves as the indicator for the hair density on a strip. –If a triangle becomes too elongated, its density is labeled as zero. Hair strands are allowed to go through sparse or broken pieces of a triangle strip more easily. Every face on a triangle strip is associated with a density value which can be zero. –The length of the triangle edges serves as the indicator for the hair density on a strip. –If a triangle becomes too elongated, its density is labeled as zero. Hair strands are allowed to go through sparse or broken pieces of a triangle strip more easily.

Modeling Collision Forces Depending on the orientation of the penetrating hair vertex and the triangular face, the repelling spring force might vary. where a is the normalized tangential vector of the hair at the penetrating vertex, b is the interpolated hair orienation on the triangular face, λ is the scale factor The scale factor λ is adjusted according to the hair density. Depending on the orientation of the penetrating hair vertex and the triangular face, the repelling spring force might vary. where a is the normalized tangential vector of the hair at the penetrating vertex, b is the interpolated hair orienation on the triangular face, λ is the scale factor The scale factor λ is adjusted according to the hair density.

Adaptive Hair Generation Generate additional guide strands adaptively on the fly to cover the over interpolated regions –Compare the distance between two guide strands. If the distance is too far, an adaptive hair is inserted. Inserted guide hairs can also be removed during the simulation Generate additional guide strands adaptively on the fly to cover the over interpolated regions –Compare the distance between two guide strands. If the distance is too far, an adaptive hair is inserted. Inserted guide hairs can also be removed during the simulation

Hair Interpolation Define a local coordinate system at each hair root Interpolate the transformed coordinates Define a local coordinate system at each hair root Interpolate the transformed coordinates translationtranslation + rotation

Random Curliness I Editing Hairs with an Offset Function

Random Curliness II Parametric Offset Function –Variable magnitude + variable period Parametric Offset Function –Variable magnitude + variable period

Examples of Curly/Wavy Hair Models

Hair Rendering Kajiya-Kay Illumination Model + Adjustable Translucency

Video: Braided Hair

Video: Long Hair

Video: Short Hair

Video: Brush

ConclusionsConclusions Hair mutual interactions are indispensable for realistic hair simulations. We use sparse guide hairs to produce hair motion, and densely interpolated hairs for the final appearance. We propose to use static links to simulate adhesive forces and enhance hairstyle recovery, and density modulated triangle strips for hair-hair collisions. Hair mutual interactions are indispensable for realistic hair simulations. We use sparse guide hairs to produce hair motion, and densely interpolated hairs for the final appearance. We propose to use static links to simulate adhesive forces and enhance hairstyle recovery, and density modulated triangle strips for hair-hair collisions.