Height and Tilt Geometric Texture

Andersen, V.; Desbrun, Mathieu; Bærentzen, Jakob Andreas; Aanæs, Henrik

doi:10.1007/978-3-642-10331-5_61

Cited by 8 publications

(10 citation statements)

References 20 publications

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“…As suggested by Andersen et al [2], applying few steps of mean curvature flow would result in a good vertexto-vertex correspondence between D and B and minimizes vertex sliding that typically occur when fairing using the umbrella operator (more details in Appendix A).…”

Section: Base Meshmentioning

confidence: 46%

“…In this work we use a signed displacement from our approximating grid to generate an image representation of the surface details. The geometric representation is similar to [2] as we compute a scalar displacement and a shift factor from a local reference frame. The shift factor allows us to deal with more complex surface details which are not possible with simple height fields.…”

Section: Parametrizationmentioning

confidence: 46%

“…Our method starts by first extracting an approximation of the surface details from a user specified part of the model. Our detail extraction is similar to recent methods [2,15] that defines details as displacements on the surface. We compute vertex displacements of the detailed mesh from a grid constructed using the smoothed base mesh.…”

Section: Overview Of Our Approachmentioning

confidence: 49%

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Detail-replicating shape stretching

2011

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Section: Base Meshmentioning

confidence: 46%

Section: Parametrizationmentioning

confidence: 46%

Section: Overview Of Our Approachmentioning

confidence: 49%

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Detail-replicating shape stretching

2011

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“…For instance, the authors of [Andersen et al 2009] used edge values to encode a "normal tilt" field over a surface: this is a vector field that defines a tilt (rotation) of the displacement direction with respect to the base normal direction. A tilt is thus a vector in the tangent space of the base shape, and its direction is the rotation axis for a rotation that transforms the displacement direction into the normal direction, and the magnitude of the tilt is the sine of the rotation angle.…”

Section: Height and Tiltmentioning

confidence: 47%

Vector field processing on triangle meshes

Goes¹,

Desbrun

Tong

2015

SIGGRAPH Asia 2015 Courses

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While scalar fields on surfaces have been staples of geometry processing, the use of tangent vector fields has steadily grown in geometry processing over the last two decades: they are crucial to encoding directions and sizing on surfaces as commonly required in tasks such as texture synthesis, non-photorealistic rendering, digital grooming, and meshing. There are, however, a variety of discrete representations of tangent vector fields on triangle meshes, and each approach offers different tradeoffs among simplicity, efficiency, and accuracy depending on the targeted application.This course reviews the three main families of discretizations used to design computational tools for vector field processing on triangle meshes: face-based, edge-based, and vertex-based representations. In the process of reviewing the computational tools offered by these representations, we go over a large body of recent developments in vector field processing in the area of discrete differential geometry. We also discuss the theoretical and practical limitations of each type of discretization, and cover increasingly-common extensions such as n-direction and n-vector fields.While the course will focus on explaining the key approaches to practical encoding (including data structures) and manipulation (including discrete operators) of finitedimensional vector fields, important differential geometric notions will also be covered: as often in Discrete Differential Geometry, the discrete picture will be used to illustrate deep continuous concepts such as covariant derivatives, metric connections, or Bochner Laplacians. PrefaceT hese course notes provide a review of the various representations of tangent vector fields on triangulated surfaces. Over the past decades, a number of approaches to express, design, and analyze vector fields on arbitrary meshes have been proposed in geometry processing, targeting a series of applications varying from rendering to animation. Some describe vector fields through values on vertices, some on edges, and some on faces; some treat vector fields as piecewise constant, some as piecewise linear, and some even involve non-linear finite elements. This lack of a unified approach to vector field representation and manipulation can be confusing for practitioners, and rare are the references that discuss the pros and cons of these various representations. The chapters in this document were written with this fact in mind, as a way to offer an introduction to the motivations, benefits, and shortcomings of the most common discretizations of vector fields in graphics-along with their associated discrete differential operators (curl, divergence, Laplacian, etc). Emphasis is placed on the tradeoffs between simplicity, efficiency, and accuracy of these geometry processing tools for applications ranging from texture synthesis to meshing.Course rationale. In many ways, this course is a continuation of ACM SIGGRAPH courses on Discrete Differential Geometry (SIGGRAPH '05 and '06, and SIGGRAPH Asia '09) and Discrete Exte...

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“…Displacement works best with simple structures such as bumps or ridges where the surface displaces along the normal. Complex structures such as serrations require specialized displacements like height-and-tilt textures [ADBA09]. In contrast, our method performs geometry replacement, which allows us to create complex, high-genus scale structures without any displacement.…”

Section: Resultsmentioning

confidence: 99%