Future work

As regards to a global view of this mesh representation with displacement map. A better ap-proach for using displacement map as a mesh representation is to catch exactly all the surface details of original mesh into displacement map and a rendering method whcih is independent with the curvature of referense surfaces.

The method to precisely catch the surface details is to ensure that every vertex on the orig-inal mesh surface maps to exact one texel of the displacement map. This requirement can be satisfied by parameterizing both the original mesh and the base mesh into a same map. But the resolution of this map should be high enough to map each original vertex to a texel. And the mapping constructed by texel correpondance should be a continuous height function for a valid displacement mapping.

For the simplification of base mesh there may be a simplification error metric designed for optimizing the displacement signals referencing to base surface. This error metric will guide the order of simplification sequence to maintain a smooth displaced surface structure mapping to the base face. Moreover, the simplification combined with the surface offsetting can be replaced with a global modeling method in a point-based or volumetric architecture.

In the parameterization stage we apply [27] under the assumption that the amount of sig-nal covered by a base face is proportion to its area. For the geometry of displaced surface has been converted to displacement signals of the base mesh. There is signal-specialized parameterization[21] developed to minimize the stretch of non-linear signals on the base face.

5.2 Future work 55 And by the proposed approach[3] we have an alternative choice to parameterize the base mesh in its finest resolution and adapt the distributions of displacement signals after each simplifica-tion step.

There are alternative methods which transform surface details into geometry signals in the frequency domaini and use wavelet decomposition to seperate the surface details with meshes’

global shape. Analyzing the surface details as frequency signals benefits a level-of-detail con-struction of the mesh representation with displacement map.

The rendering methods[9][19][25] with displacement mapping generate good rendering re-sults in real time. But since the ray-tracing process is transformed to the texture space not within object space. Rendering distortions caused by this transformation rise when the trac-ing of view-ray cross from a base face’s tangent space into another base face’s tangent space.

Although we use the linear interpolated transformation to avoid this jiggling on the rendering result, the viewing distortion is still apparent when the tracing is along a winding curve on the surface. An adaptive searching step size and searching direction along the view-ray may be a better solution of this problem.

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