3.1 Continuous Data3.1.1 What Is Continuous Data?3.1.2 Mathematical Continuity3.1.3 Dimensions: Geometry, Topology, and Attributes3.2 Sampled DataInterpolationGrids and cellsPutting it all together3.3 Discrete Datasets3.4 Cell Types3.4.1 Vertex3.4.2 Line3.4.3 Triangle3.4.4 Quad3.4.5 Tetrahedron3.4.6 Hexahedron3.4.7 Other Cell Types3.5 Grid Types3.5.1 Uniform Grids3.5.2 Rectilinear Grids3.5.3 Structured Grids3.5.4 Unstructured Grids3.6 Attributes3.6.1 Scalar Attributes3.6.2 Vector Attributes3.6.3 Color AttributesRGB spaceHSV spaceConverting between RGB and HSVColor perception3.6.4 Tensor AttributesCurvature as a tensorTensors, vectors, and scalars3.6.5 Non-Numerical Attributes3.6.6 Properties of Attribute DataCompletenessMultivariate dataNode vs. cell attributesHigh-variate interpolationNormalsVectorsColorsTensors3.7 Computing Derivatives of Sampled Data3.8 Implementation3.8.1 Grid ImplementationUniform gridsRectilinear gridsStructured gridsUnstructured grids3.8.2 Attribute Data ImplementationScalar attributesVector attributesStoring several attribute instances3.9 Advanced Data Representation3.9.1 Data ResamplingCell to vertex resamplingVertex to cell resamplingSubsampling and supersampling3.9.2 Scattered Point InterpolationConstructing a grid from scattered pointsGridless interpolationPerformance issuesShepard interpolation3.10 ConclusionFigure 3.1Figure 3.2Figure 3.3Figure 3.4Figure 3.5Figure 3.6Figure 3.7Figure 3.8Figure 3.9Figure 3.10Figure 3.11Figure 3.12Figure 3.13Figure 3.14Figure 3.15Figure 3.16Figure 3.17Figure 3.18Figure 3.19Table 3.1Table 3.2Listings 3.1Listings 3.2Listings 3.3Listings 3.4Listings 3.5Listings 3.6Listings 3.7Listings 3.8Listings 3.9Listings 3.10Listings 3.11Listings 3.12