We introduce an algorithm to remesh triangle meshes representing developable surfaces to planar quad dominant meshes. The output of our algorithm consists of planar quadrilateral (PQ) strips that are aligned to principal curvature directions and closely approximate the curved parts of the input developable, and planar polygons representing the flat parts of the input. Developable PQ-strip meshes are useful in many areas of shape modeling, thanks to the simplicity of fabrication from flat sheet material. Unfortunately, they are difficult to model due to their restrictive combinatorics and locking issues. Other representations of developable surfaces, such as arbitrary triangle or quad meshes, are more suitable for interactive freeform modeling, but generally have non-planar faces or are not aligned to principal curvatures. Our method leverages the modeling flexibility of non-ruling based representations of developable surfaces, while still obtaining developable, curvature aligned PQ-strip meshes. Our algorithm optimizes for a scalar function on the input mesh, such that its level sets are extrinsically straight and align well to the locally estimated ruling directions. The condition that guarantees straight level sets is nonlinear of high order and numerically difficult to enforce in a straightforward manner. We devise an alternating optimization method that makes our problem tractable and practical to compute. Our method works automatically on any developable input, including multiple patches and curved folds, without explicit domain decomposition. We demonstrate the effectiveness of our approach on a variety of developable surfaces and show how our remeshing can be used alongside handle based interactive freeform modeling of developable shapes.
翻译:我们引入了一种算法, 代表成形三角间距, 代表可成形表面, 代表可成形表面, 以平面 平面 平面 。 我们的算法输出由一些平面 组成。 我们的算法由一些代表输入平面 的折叠三角形( PQ) 组成。 我们的算法产出由一些代表可成形模型的许多领域组成。 不幸的是, 它们很难建模, 因为它们具有限制性的组合和锁定问题。 其它可成形的四边形( PQ) 条条条线( PQ), 与主曲形方向相匹配, 与主要的曲线方向相匹配, 但一般是非平面的曲线, 或与输入的曲形多边形( PQ) 相匹配。 我们的方法利用基于非鲁莽的表层演示灵活性, 但仍能获得可成形的、 曲曲直曲直方向( Q- stri) 方法的基础。 我们的算法可以优化在输入的模型和锁定的变形模型上, 任意三角或折形( 折形) 等直线路路的表面, 将显示我们的平面的平面的平面的平面的平面的平面的排序, 显示不直方向( ) 将显示的平面的平面的平流, 显示我们方的平面的平面的平面的平面的平面的平面的平面的平向, 的平面的平向, 显示的平面的平面的平面的平面的平向的平面的平面的平面的平面的平面的平面的平向,, 显示着的平向的平面的平面的平面的平面的平面的平面的平面的平。