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Hey, I'm the blender dev "Genscher" but my real last name is "Genrich" :) I corrected that. Otherwise this is an awesome recap!
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Summary: Initially in 2004, Todd Koeckeritz leveraged Provot's Cloth Model (Deformation Constraints in a Mass-Spring Model to Describe Rigid Cloth Behavior); also, he leveraged simplified portions of Provot's Cloth Collision Model (Collision and self-collision handling in cloth model dedicated to design garments). Then in 2006, Daniel GenscherGenrich completed an implementation of Mezger's Cloth Collision Model (Improved Collision Detection and Response Techniques for Cloth Animation). Additionally, Todd Koeckeritz created a parameter named "Steps"/"Quality" to handle time steps. Finally in 2008, Daniel GenscherGenrich released Blender Cloth (according to BlenderNation.com).

The initial checkin of Blender Cloth files for "trunk/blender/source/blender/makesdna/DNA_cloth_types.h" by Daniel GenscherGenrich (Contributor of Blender Cloth) reads in September 2007:

Todd Koeckeritz talks about Daniel Genscher'sGenrich implementation of Mezger's Cloth Collision Model in March/April 2006:

In April 2006, Todd Koeckeritz called it "Steps". Between September 2007 and January 2008, Daniel GensherGenrich renamed "Steps Per Frame" to "Quality". The following code diff of "/source/blender/src/buttons_object.c" represents these changes:

Daniel GenscherGenrich simplified the controls by May 2008:

Summary: Initially in 2004, Todd Koeckeritz leveraged Provot's Cloth Model (Deformation Constraints in a Mass-Spring Model to Describe Rigid Cloth Behavior); also, he leveraged simplified portions of Provot's Cloth Collision Model (Collision and self-collision handling in cloth model dedicated to design garments). Then in 2006, Daniel Genscher completed an implementation of Mezger's Cloth Collision Model (Improved Collision Detection and Response Techniques for Cloth Animation). Additionally, Todd Koeckeritz created a parameter named "Steps"/"Quality" to handle time steps. Finally in 2008, Daniel Genscher released Blender Cloth (according to BlenderNation.com).

The initial checkin of Blender Cloth files for "trunk/blender/source/blender/makesdna/DNA_cloth_types.h" by Daniel Genscher (Contributor of Blender Cloth) reads in September 2007:

Todd Koeckeritz talks about Daniel Genscher's implementation of Mezger's Cloth Collision Model in March/April 2006:

In April 2006, Todd Koeckeritz called it "Steps". Between September 2007 and January 2008, Daniel Gensher renamed "Steps Per Frame" to "Quality". The following code diff of "/source/blender/src/buttons_object.c" represents these changes:

Daniel Genscher simplified the controls by May 2008:

Summary: Initially in 2004, Todd Koeckeritz leveraged Provot's Cloth Model (Deformation Constraints in a Mass-Spring Model to Describe Rigid Cloth Behavior); also, he leveraged simplified portions of Provot's Cloth Collision Model (Collision and self-collision handling in cloth model dedicated to design garments). Then in 2006, Daniel Genrich completed an implementation of Mezger's Cloth Collision Model (Improved Collision Detection and Response Techniques for Cloth Animation). Additionally, Todd Koeckeritz created a parameter named "Steps"/"Quality" to handle time steps. Finally in 2008, Daniel Genrich released Blender Cloth (according to BlenderNation.com).

The initial checkin of Blender Cloth files for "trunk/blender/source/blender/makesdna/DNA_cloth_types.h" by Daniel Genrich (Contributor of Blender Cloth) reads in September 2007:

Todd Koeckeritz talks about Daniel Genrich implementation of Mezger's Cloth Collision Model in March/April 2006:

In April 2006, Todd Koeckeritz called it "Steps". Between September 2007 and January 2008, Daniel Genrich renamed "Steps Per Frame" to "Quality". The following code diff of "/source/blender/src/buttons_object.c" represents these changes:

Daniel Genrich simplified the controls by May 2008:

spelling error fixed
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Luis B
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Summary: Initially in 2004, Todd Koeckeritz leveraged Provot's Cloth Model (Deformation Constraints in a Mass-Spring Model to Describe Rigid Cloth Behavior); also, he leveraged simplfiedsimplified portions of Provot's Cloth Collision Model (Collision and self-collision handling in cloth model dedicated to design garments). Then in 2006, Daniel Genscher completed an implementation of Mezger's Cloth Collision Model (Improved Collision Detection and Response Techniques for Cloth Animation). Additionally, Todd Koeckeritz created a parameter named "Steps"/"Quality" to handle time steps. Finally in 2008, Daniel Genscher released Blender Cloth (according to BlenderNation.com).

Summary: Initially in 2004, Todd Koeckeritz leveraged Provot's Cloth Model (Deformation Constraints in a Mass-Spring Model to Describe Rigid Cloth Behavior); also, he leveraged simplfied portions of Provot's Cloth Collision Model (Collision and self-collision handling in cloth model dedicated to design garments). Then in 2006, Daniel Genscher completed an implementation of Mezger's Cloth Collision Model (Improved Collision Detection and Response Techniques for Cloth Animation). Additionally, Todd Koeckeritz created a parameter named "Steps"/"Quality" to handle time steps. Finally in 2008, Daniel Genscher released Blender Cloth (according to BlenderNation.com).

Summary: Initially in 2004, Todd Koeckeritz leveraged Provot's Cloth Model (Deformation Constraints in a Mass-Spring Model to Describe Rigid Cloth Behavior); also, he leveraged simplified portions of Provot's Cloth Collision Model (Collision and self-collision handling in cloth model dedicated to design garments). Then in 2006, Daniel Genscher completed an implementation of Mezger's Cloth Collision Model (Improved Collision Detection and Response Techniques for Cloth Animation). Additionally, Todd Koeckeritz created a parameter named "Steps"/"Quality" to handle time steps. Finally in 2008, Daniel Genscher released Blender Cloth (according to BlenderNation.com).

fix statements about damping
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Luis B
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As of today (April 2015), the controls for Blender have three damping forces (VelocitySpring, SpringVelocity, Air). Provot's model explains these three damping forces as follows (respectively: Internal, Gravity, Viscous Damping, Air-Damping/Air):

The internal force is the resultant of the tensions of the springs linking P_ij to its neighbors. The external force is of various nature according according to the kind of load to to which we wish the model to be exposed exposed. Omnipresent loads will be gravity gravity, a viscous damping, and a viscous viscous interaction with an air stream stream or wind. (1) Let g be the acceleration acceleration of gravity, the weight of of P_ij is given by F_g=mg. (2) The viscous viscous damping will be given by F_d= F_d=-C_dv where C_d is a damping coefficient coefficient and v is the velocity of point point P_ij. The role of this damping damping is in fact to model in first approximation approximation the dissipation of the the mechanical energy of our model. It It is introduced as an external force force but could actually be considered as as an internal force as well. (3) Finally Finally, a viscous fluid moving at a uniform uniform velocity u exerts on the surface surface of a body moving at a velocity velocity v a force F_v = C_v((n dot    (u-v))n where n is the unit normal on on the surface.

As of today (April 2015), the controls for Blender have three damping forces (Velocity, Spring, Air). Provot's model explains these three damping forces as follows (respectively: Gravity, Viscous Damping, Air):

The external force is of various nature according to the kind of load to which we wish the model to be exposed. Omnipresent loads will be gravity, a viscous damping, and a viscous interaction with an air stream or wind. (1) Let g be the acceleration of gravity, the weight of P_ij is given by F_g=mg. (2) The viscous damping will be given by F_d=-C_dv where C_d is a damping coefficient and v is the velocity of point P_ij. The role of this damping is in fact to model in first approximation the dissipation of the mechanical energy of our model. It is introduced as an external force but could actually be considered as an internal force as well. (3) Finally, a viscous fluid moving at a uniform velocity u exerts on the surface of a body moving at a velocity v a force F_v = C_v((n dot  (u-v))n where n is the unit normal on the surface.

As of today (April 2015), the controls for Blender have three damping forces (Spring, Velocity, Air). Provot's model explains these three damping forces as follows (respectively: Internal, Gravity, Viscous-Damping/Air):

The internal force is the resultant of the tensions of the springs linking P_ij to its neighbors. The external force is of various nature according to the kind of load to which we wish the model to be exposed. Omnipresent loads will be gravity, a viscous damping, and a viscous interaction with an air stream or wind. Let g be the acceleration of gravity, the weight of P_ij is given by F_g=mg. The viscous damping will be given by F_d=-C_dv where C_d is a damping coefficient and v is the velocity of point P_ij. The role of this damping is in fact to model in first approximation the dissipation of the mechanical energy of our model. It is introduced as an external force but could actually be considered as an internal force as well. Finally, a viscous fluid moving at a uniform velocity u exerts on the surface of a body moving at a velocity v a force F_v = C_v((n dot  (u-v))n where n is the unit normal on the surface.

reorg and reword for damping params
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Luis B
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wording about protov paper in summary
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Luis B
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wording for quality/steps
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Luis B
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remove commas
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Luis B
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wording
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Luis B
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add links for research papers
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Luis B
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fixed wording
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Luis B
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information about cloth parameters
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Luis B
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quality steps relationship
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Luis B
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re-org
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Luis B
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Luis B
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