Surface Deformation Potentials on Meshes for Computer Graphics and Visualization

Dissertation, Universität Bonn, Oct. 2011
 

Abstract

Shape deformation models have been used in computer graphics primarily to describe the dynamics of physical deformations like cloth draping, collisions of elastic bodies, fracture, or animation of hair. Less frequent is their application to problems not directly related to a physical process. In this thesis we apply deformations to three problems in computer graphics that do not correspond to physical deformations. To this end, we generalize the physical model by modifying the energy potential. Originally, the energy potential amounts to the physical work needed to deform a body from its rest state into a given configuration and relates material strain to internal restoring forces that act to restore the original shape. For each of the three problems considered, this potential is adapted to reflect an application specific notion of shape. Under the influence of further constraints, our generalized deformation results in shapes that balance preservation of certain shape properties and application specific objectives similar to physical equilibrium states.

The applications discussed in this thesis are surface parameterization, interactive shape editing and automatic design of panorama maps. For surface parameterization, we interpret parameterizations over a planar domain as deformations from a flat initial configuration onto a given surface. In this setting, we review existing parameterization methods by analyzing properties of their potential functions and derive potentials accounting for distortion of geometric properties.

Interactive shape editing allows an untrained user to modify complex surfaces, be simply grabbing and moving parts of interest. A deformation model interactively extrapolates the transformation from those parts to the rest of the surface. This thesis proposes a differential shape representation for triangle meshes leading to a potential that can be optimized interactively with a simple, tailored algorithm. Although the potential is not physically accurate, it results in intuitive deformation behavior and can be parameterized to account for different material properties.

Panorama maps are blends between landscape illustrations and geographic maps that are traditionally painted by an artist to convey geographic surveyknowledge on public places like ski resorts or national parks. While panorama maps are not drawn to scale, the shown landscape remains recognizable and the observer can easily recover details necessary for self location and orientation. At the same time, important features as trails or ski slopes appear not occluded and well visible. This thesis proposes the first automatic panorama generation method. Its basis is again a surface deformation, that establishes the necessary compromise between shape preservation and feature visibility.

(Thesis submission date: Jan . 2010)

Download: http://hss.ulb.uni-bonn.de/2011/2641/2641-engl.htm

Bibtex

@PHDTHESIS{degener-2011-dissertation,
    author = {Degener, Patrick},
     title = {Surface Deformation Potentials on Meshes for Computer Graphics and Visualization},
      type = {Dissertation},
      year = {2011},
     month = oct,
    school = {Universit{\"a}t Bonn},
  abstract = {Shape deformation models have been used in computer graphics primarily to describe the dynamics of
              physical deformations like cloth draping, collisions of elastic bodies, fracture, or animation of
              hair. Less frequent is their application to problems not directly related to a physical process. In
              this thesis we apply deformations to three problems in computer graphics that do not correspond to
              physical deformations. To this end, we generalize the physical model by modifying the energy
              potential. Originally, the energy potential amounts to the physical work needed to deform a body
              from its rest state into a given configuration and relates material strain to internal restoring
              forces that act to restore the original shape. For each of the three problems considered, this
              potential is adapted to reflect an application specific notion of shape. Under the influence of
              further constraints, our generalized deformation results in shapes that balance preservation of
              certain shape properties and application specific objectives similar to physical equilibrium states.
              
              The applications discussed in this thesis are surface parameterization, interactive shape editing
              and automatic design of panorama maps. For surface parameterization, we interpret parameterizations
              over a planar domain as deformations from a flat initial configuration onto a given surface. In this
              setting, we review existing parameterization methods by analyzing properties of their potential
              functions and derive potentials accounting for distortion of geometric properties.
              
              Interactive shape editing allows an untrained user to modify complex surfaces, be simply grabbing
              and moving parts of interest. A deformation model interactively extrapolates the transformation from
              those parts to the rest of the surface. This thesis proposes a differential shape representation for
              triangle meshes leading to a potential that can be optimized interactively with a simple, tailored
              algorithm. Although the potential is not physically accurate, it results in intuitive deformation
              behavior and can be parameterized to account for different material properties.
              
              Panorama maps are blends between landscape illustrations and geographic maps that are traditionally
              painted by an artist to convey geographic surveyknowledge on public places like ski resorts or
              national parks. While panorama maps are not drawn to scale, the shown landscape remains recognizable
              and the observer can easily recover details necessary for self location and orientation. At the same
              time, important features as trails or ski slopes appear not occluded and well visible. This thesis
              proposes the first automatic panorama generation method. Its basis is again a surface deformation,
              that establishes the necessary compromise between shape preservation and feature visibility.},
       url = {http://hss.ulb.uni-bonn.de/2011/2641/2641-engl.htm}
}