The journey to achieving 3D has been a multifaceted and winding path, driven not by a deliberate plan but rather by the natural progression of discoveries fueled by intellectual curiosity, genius, and occasional chance findings. When examining the history of any subject, it’s essential to consider the timeline and key milestones. In tracing the development of 3D, we find that it is built upon the foundation of basic geometry, with the triangle being the fundamental building block of computer graphics. However, before triangles, humans had to develop the ability to count, which led to the establishment of numbering systems dating back to around 5000 BCE. These systems required rules to ensure predictability and repeatability, laying the groundwork for more complex mathematical concepts. The development of linguistics also played a crucial role, as seen in the work of Panini, who established the Sanskrit grammar and the Ashtadhyayi, marking the beginning of linguistic studies. The need to share counting systems and geometric designs with others drove the dissemination of knowledge across cultures. Thales of Miletos, for instance, brought the science of geometry from Egypt to Greece three centuries before Euclid, while Pythagoras utilized these concepts to develop the Pythagorean theorem. The introduction of deductive reasoning by Thales and its organization by Euclid in “The Elements” further solidified the foundations of geometry. The understanding and utilization of zero, negative numbers, matrix math, and transformations were also critical steps in this journey. It took nearly 6000 years to develop a comprehensive understanding of 2D geometry, and extending this knowledge to 3D proved to be a significant challenge. Heron of Alexandria successfully mastered 3D geometry in the first century, demonstrating the complexity and nuance involved in this progression.

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Getting to 3D

  • Jon Peddie

摘要

The journey to achieving 3D has been a multifaceted and winding path, driven not by a deliberate plan but rather by the natural progression of discoveries fueled by intellectual curiosity, genius, and occasional chance findings. When examining the history of any subject, it’s essential to consider the timeline and key milestones. In tracing the development of 3D, we find that it is built upon the foundation of basic geometry, with the triangle being the fundamental building block of computer graphics. However, before triangles, humans had to develop the ability to count, which led to the establishment of numbering systems dating back to around 5000 BCE. These systems required rules to ensure predictability and repeatability, laying the groundwork for more complex mathematical concepts. The development of linguistics also played a crucial role, as seen in the work of Panini, who established the Sanskrit grammar and the Ashtadhyayi, marking the beginning of linguistic studies. The need to share counting systems and geometric designs with others drove the dissemination of knowledge across cultures. Thales of Miletos, for instance, brought the science of geometry from Egypt to Greece three centuries before Euclid, while Pythagoras utilized these concepts to develop the Pythagorean theorem. The introduction of deductive reasoning by Thales and its organization by Euclid in “The Elements” further solidified the foundations of geometry. The understanding and utilization of zero, negative numbers, matrix math, and transformations were also critical steps in this journey. It took nearly 6000 years to develop a comprehensive understanding of 2D geometry, and extending this knowledge to 3D proved to be a significant challenge. Heron of Alexandria successfully mastered 3D geometry in the first century, demonstrating the complexity and nuance involved in this progression.