Enrique Alberto Rosales Ruiz

A Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Computer Science in the field of Computer Graphics

Graduate School
Instituto Tecnológico y de Estudios Superiores de Monterrey
May 8, 2013

This thesis presents a new geometrical method to solve the inverse kinematics (IK) problem for characters with highly articulated limbs. This method relies on a new triangle theorem, which is the main contribution of this work. This theorem, allows to compute the intersection between two circles, without any sine or cosine computation, and in less time than the classic algebraic approach. Applying this new method, it is possible to produce complex shapes as spirals or springs, with stable and smooth animations, in kinematic chains (KC) with hundreds of links. The proposed method can be also applied in many different geometry problems, such as Voronoi diagrams and others, making it an important contribution to computer science. This work was awarded as most outstanding thesis of 2013 ITESM MSCS generation.

The main purpose of this work is to develop a new way to animate characters with highly articulated limbs like the spider at left, while keeping curves ratios and smooth movements. This kind of animations, needs to be solved in very short production times, and the IK tools that are available in most 3D packages, require a lot of setup time in the case of complex shapes. Also, for a very redundant kinematic chain, it is very difficult to obtain a smooth animation automatically. So. in many cases, the animation has to be done by rotating and moving each link separately, for each animation frame.

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Thesis file

Dowload the Article published at ICGG 2014

Thanks to Luis E. Falcón-Morales for being my thesis advisor, I couldn’t have done this work without his help. Thanks to Alejandro García, Joel C. Huegel, Josué S. Reynoso and Gabriel Castillo for supporting the development of the original idea of this work. I am grateful to Raquel Ruiz de Equino and Sergio Velázquez Rodríguez for their help with the theorem proof. My thanks to Luis E. Mercado for his help in developing sections 4.2 and 4.3. I gratefully appreciate Guillermo A. Parra for a careful reading and helpful comments on my earlier thesis proposal. Thanks to Arturo Jafet Rodríguez for building the LaTeX configuration files used in this thesis. My thanks to Instituto Jaliscience de la Juventud, Instituto Tecnológico y de Estudios Superiores de Monterrey and Universidad Panamericana, for supporting the scholarship that allowed me to study my Master Degree. I am deeply grateful to my wife Elinor Palomares and all my family for giving me the support needed to complete this project. And of course, many thanks to my thesis committee for providing invaluable feedback for refining this work.

All images copyright of Enrique Rosales © or their respective owners 1998 - 2020

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