作者：Benjamin Kenwright
计算机图形学和几何领域中的变换是在二维和三维空间中有效操纵和控制对象的最重要概念之一。变革有多种形式，每种形式都有其优点和缺点。对偶四元数是以统一形式表示变换的一个特别强大的工具。这种统一形式的优点是插值财产，它解决了一系列模拟问题（紧凑形式允许旋转和平移组件耦合）。在本文中，我们研究了各种对偶四元数插值选项，这些选项在计算成本、美学因素和耦合依赖性之间实现了不同的权衡。令人惊讶的是，尽管双四元数是图形库中的一种常见工具，但插值细节有限。在这里，我们试图解释插值概念，详细阐述基础理论，同时解释插值的概念和定制修改
Transformations in the field of computer graphics and geometry are one of themost important concepts for efficient manipulation and control of objects in2-dimensional and 3-dimensional space. Transformations take many forms eachwith their advantages and disadvantages. A particularly powerful tool forrepresenting transforms in a unified form are dual-quaternions. A benefit ofthis unified form is the interpolation properties, which address a range oflimitations (compact form that allows a rotational and translational componentsto be coupled). In this article, we examine various dual-quaternioninterpolation options that achieve different trade-offs between computationalcost, aesthetic factors and coupling dependency. Surprisingly, despitedual-quaternions being a common tool in graphics libraries, there are limiteddetails on the interpolation details. Here we attempt to explain interpolationconcept, elaborating on underpinning theories, while explaining concepts andbespoke modifications for added control.
论文链接：http://arxiv.org/pdf/2303.13395v1
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