Fast and resolution independent line integral convolution
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Fast line integral convolution for arbitrary surfaces in 3D
Visualization and mathematics
Applications of pixel textures in visualization and realistic image synthesis
I3D '99 Proceedings of the 1999 symposium on Interactive 3D graphics
Interactive exploration of volume line integral convolution based on 3D-texture mapping
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
C1-interpolation for vector field topology visualization
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
A topology simplification method for 2D vector fields
Proceedings of the conference on Visualization '00
Texture synthesis over arbitrary manifold surfaces
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Meshed atlases for real-time procedural solid texturing
ACM Transactions on Graphics (TOG)
Image based flow visualization
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
IEEE Transactions on Visualization and Computer Graphics
Visualizing Nonlinear Vector Field Topology
IEEE Transactions on Visualization and Computer Graphics
Higher Order Singularities in Piecewise Linear Vector Fields
Proceedings of the 9th IMA Conference on the Mathematics of Surfaces
ISA and IBFVS: Image Space-Based Visualization of Flow on Surfaces
IEEE Transactions on Visualization and Computer Graphics
Image Space Based Visualization of Unsteady Flow on Surfaces
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Image Space Advection on graphics hardware
Proceedings of the 21st spring conference on Computer graphics
Vector field design on surfaces
ACM Transactions on Graphics (TOG)
Periodic global parameterization
ACM Transactions on Graphics (TOG)
Generalized Streak Lines: Analysis and Visualization of Boundary Induced Vortices
IEEE Transactions on Visualization and Computer Graphics
N-symmetry direction field design
ACM Transactions on Graphics (TOG)
Geometry-aware direction field processing
ACM Transactions on Graphics (TOG)
Complete tensor field topology on 2D triangulated manifolds embedded in 3D
EuroVis'11 Proceedings of the 13th Eurographics / IEEE - VGTC conference on Visualization
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Accurately representing higher-order singularities of vector fields defined on piecewise linear surfaces is a non-trivial problem. In this work, we introduce a concise yet complete interpolation scheme of vector fields on arbitrary triangulated surfaces. The scheme enablesarbitrary singularities to be represented at vertices} The representation can be considered as a facet-based "encoding" of vector fields on piecewise linear surfaces. The vector field is described in polar coordinates over each facet, with a facet edge being chosen as the reference to define the angle. An integer called theperiod jump is associated to each edge of the triangulation to remove the ambiguity when interpolating the direction of the vector fieldbetween two facets that share an edge. To interpolate the vector field, we first linearlyinterpolate the angle of rotation of the vectors along the edges of the facet graph. Then, we use a variant ofNielson's side-vertex scheme to interpolate the vector field over the entire surface. With our representation, we remove the bound imposed on the complexity of singularities that a vertex can represent by its connectivity. This boundis a limitation generally exists in vertex-based linear schemes. Furthermore, using our data structure, the index of a vertex of a vector field can be combinatorily determined.We show the simplicity of the interpolation scheme with a GPU-accelerated algorithm for a LIC-based visualization of the so-defined vector fields, operating in image space. We demonstrate the algorithm applied to various vector fields on curved surfaces.