Contour map principal curvatures postview
![contour map principal curvatures postview contour map principal curvatures postview](http://www.compassdude.com/i/contour-map.gif)
This means that some energyįunction is required, and an effective choice is the integral absolute mean curvature Loop over all edges and flip if it reduces some energy.
![contour map principal curvatures postview contour map principal curvatures postview](https://www.pumper.com/uploads/images/contour-maps-3.gif)
The edge sharedīy two adjacent triangles can be replaced by a transverse edge. The most popular way of doing this is by edge flipping. In some cases, we wish to improve a triangulation while maintaining the vertices Very often these strokes are aligned with the directions of min or max Is “hatching” where the artist draws strokes in order to enhance shape and One artistic style that has been simulated Ren-dering of 3D models in an artistic fashion.
![contour map principal curvatures postview contour map principal curvatures postview](https://media.cheggcdn.com/study/03c/03c2e185-7d94-4e44-a753-75e4ea6ff776/image.png)
Small curvature variations may not be obviousįrom a shaded rendition of 3D model but are easy to detect if the curvature is mappedĪ related area is non-photorealistic rendering which is concerned with the The most obvious application of curvature measures on triangle meshes is simply Geometric properties of meshes still appear. That this is an active area of research, and new methods for computing differential Latter is similar but not identical to the method discussed in Sect. Operator were proposed by Taubin and by Hildebrandt and Polthier. Two methods (which were not discussed here) for estimating the shape propose a systematic framework for estimating curvatures from Prob-ably a good starting point for a more in-depth look at the literature is where construct meshes from known smooth surfaces and compare the estimatedĬlearly, not all techniques for estimating curvature have been discussed. 8.6įor an interesting comparison of curvature estimation methods see. The shape operators at each vertex were averaged with their neighbors to smoothen the field, and then the eigensolutions were found as discussed in Sect. The directions were estimated using the di-hedral angle method from Sect. 8.8 The min curvature directions of the bunny. Once the principal curvatures have been computed, it is easy to find the Gaußianįig. Note, though, that if the dihedral angle method from Sect.8.4was used toĮs-timate the shape operator, the directions are flipped so that the eigenvectorĬorre-sponding to the greatest eigenvalue is the direction of minimal curvature. If S is a 2×2 matrix, the eigensolutions simply correspond to the principal Is clearly planar and the principal directions are not defined. (eigen-vector) will give the second principal direction. However, if we know the normal (which can easily beĮstimated) the cross product of the normal and the first principal direction If one of the principalĬurvatures is zero, it is clearly not possible to distinguish between the principalĭirection and the normal. The two remainingĮigenso-lutions correspond to the principal curvatures and directions. Zero due to numerical issues) is the normal direction. Numer-ically smallest eigenvalue (it should be zero, but it is possible that it is not exactly If S is represented as a 3×3 matrix, the eigenvector corresponding to the Methods for computing eigensolutions rely on the matrix being symmetric. However, the methods which we have discussedĪbove both produce symmetric shape operators. Note that S is not necessarily symmetric-thisĭepends on the parametrization. 8.8) is reduced to finding theĮigenvalues and eigenvectors of S. Of minimum curvature directions is shown in Fig. Of finding the principal curvatures and the corresponding directions (an example Given a shape operator, S, represented as either a 2×2 or 3×3 matrix, the problem It is also straightforward to transform S into a 3×3įor a more detailed discussion of the method above, the reader is referred toĨ.6 Estimating Principal Curvatures and Directions From S, the principal curvatures and directions at the point p i can be computed asĭiscussed in the next section.