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: