We present a novel approach for solving articulated inverse kinematic problems (e.g., character structures) by means of an iterative dual-quaternion and exponentialmapping approach. As dual-quaternions are a break from the norm and offer a straightforward and computationally efficient technique for representing kinematic transforms (i.e., position and translation). Dual-quaternions are capable of represent both translation and rotation in a unified state space variable with its own set of algebraic equations for concatenation and manipulation. Hence, an articulated structure can be represented by a set of dual-quaternion transforms, which we can manipulate using inverse kinematics (IK) to accomplish specific goals (e.g., moving end-effectors towards targets). We use the projected Gauss-Seidel iterative method to solve the IK problem with joint limits. Our approach is flexible and robust enough for use in interactive applications, such as games. We use numerical examples to demonstrate our approach, which performed successfully in all our test cases and produced pleasing visual results.
翻译:我们提出了一个新颖的方法,通过迭代双向和指数映射方法解决分辨反动向问题(例如字符结构),因为双向结构与规范脱节,提供了代表运动变异(即位置和翻译)的直截了当和计算效率高的技术。双向结构能够在一个统一的州空间变量中代表翻译和轮换,并配有一套用于交配和操控的代数方程式。因此,一个分立结构可以通过一套双向结构变异来代表,我们可以用反向运动变异(IK)实现具体目标(例如,将终端效应向目标移动)。我们用预测的高斯-Seidel迭接合方法解决IK问题。我们的方法足够灵活和有力,足以用于互动应用,例如游戏。我们用数字例子来展示我们的方法,我们的方法在所有测试案例中都成功进行,并产生令人愉快的视觉结果。