{"id":228,"date":"2024-04-25T23:23:51","date_gmt":"2024-04-25T23:23:51","guid":{"rendered":"https:\/\/croakthecode.tcu.edu\/nguyen\/?p=228"},"modified":"2024-05-06T20:18:26","modified_gmt":"2024-05-06T20:18:26","slug":"how-to-code-donut-shaped-c-code-that-generates-a-3d-spinning-donut","status":"publish","type":"post","link":"https:\/\/croakthecode.tcu.edu\/nguyen\/2024\/04\/25\/how-to-code-donut-shaped-c-code-that-generates-a-3d-spinning-donut\/","title":{"rendered":"how to: code donut-shaped C code that generates a 3D spinning donut"},"content":{"rendered":"\n

When I thought of coding tutorial, I know I must a post on donut-shaped C code that generates a 3D spinning donut. It’s just so legendary that you have to know it.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Although I’m good at math in highschool, I haven\u2019t touched math for the last 3 years. In this post, instead of bombing with code, I will help you understand the process and the match behind this masterpiece.<\/p>\n\n\n\n

donut-shaped C code that generates a 3D spinning donut<\/h2>\n\n\n\n

anh’s note from reading Math Behind Donut Shape C Code<\/a><\/strong><\/em> by whoisslimshady<\/strong> and Donut Math: Make a 3D spinning torus with C<\/a><\/em><\/strong> by Shreyos Ghosh<\/strong>:<\/p>\n\n\n\n

Mathematical Background:<\/strong><\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n
    \n
  • 3D Projection:<\/strong>\n
      \n
    • Projecting 3D coordinates onto a 2D plane by scaling a coordinate by a screen distance constant, denoted as \ud835\udc3e1K<\/em>1\u200b.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • Rotation Matrix:<\/strong>\n
        \n
      • Rotating a point in 3D space involves matrix multiplications. In this case, rotation around the y-axis is utilized.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n

        Drawing the Torus:<\/strong><\/p>\n\n\n\n

        \"\"<\/figure>\n\n\n\n
          \n
        • Torus Construction:<\/strong>\n
            \n
          • A torus is formed by revolving a circle of radius \ud835\udc452R<\/em>2\u200b around a line generated by a bigger circle of radius \ud835\udc451R<\/em>1\u200b.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
          • Point Rotation:<\/strong>\n
              \n
            • Each point on the circle with radius \ud835\udc452R<\/em>2\u200b is rotated by an angle \ud835\udf19\u03d5<\/em>, and the circle is rotated by an angle \ud835\udf03\u03b8<\/em>.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
            • Rotation Matrices:<\/strong>\n
                \n
              • Utilizing rotation matrices, points are rotated around the y-axis and additional axes if required.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n

                3D Projection and Illumination:<\/strong><\/p>\n\n\n\n

                \"\"<\/figure>\n\n\n\n
                  \n
                • Depth Adjustment:<\/strong>\n
                    \n
                  • To move the torus in front of the viewer, a constant \ud835\udc3e\u2032K<\/em>\u2032 is added to the Z-coordinate.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                  • Projection Formulas:<\/strong>\n
                      \n
                    • The 3D coordinates are projected onto the 2D screen with adjustments based on constants \ud835\udc3e1K<\/em>1\u200b and \ud835\udc3e\u2032K<\/em>\u2032.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                    • Illuminance Calculation:<\/strong>\n
                        \n
                      • Illuminance is determined by the dot product of the surface normal and the chosen lighting direction.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n

                        Coding the Donut:<\/strong><\/p>\n\n\n\n

                        \"\"
                        photo for reference and great motivation. credit: Unsplash\/Fahim Mohammed<\/figcaption><\/figure>\n\n\n\n
                          \n
                        • Headers Used:<\/strong>\n
                            \n
                          • The necessary libraries like <stdio.h><\/code> and <math.h><\/code> are included.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                          • Variables Initialization:<\/strong>\n
                              \n
                            • Various constants and variables for screen resolution, rotation angles, and buffer size are declared.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                            • Custom Functions:<\/strong>\n
                                \n
                              • render_frame()<\/code> calculates pixel positions and illuminance.<\/li>\n\n\n\n
                              • display()<\/code> outputs the rendered frame to the console.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n

                                Final Code Execution:<\/strong><\/p>\n\n\n\n

                                  \n
                                • Loop Execution:<\/strong>\n
                                    \n
                                  • The code repeatedly generates and displays frames, updating rotation angles for animation.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                                  • ASCII Art Implementation:<\/strong>\n
                                      \n
                                    • Pixels are represented by ASCII characters based on illuminance levels, producing a donut-like shape.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n
                                      \"\"<\/figure>\n\n\n\n

                                      Understanding the Code:<\/strong><\/p>\n\n\n\n

                                      \"\"
                                      I feel you bro. Didn’t know what I got myself into.<\/figcaption><\/figure>\n\n\n\n
                                        \n
                                      • Framebuffer Approach:<\/strong>\n
                                          \n
                                        • The code utilizes a framebuffer and a Z-buffer to render ASCII art of the donut.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                                        • Pixel Plotting:<\/strong>\n
                                            \n
                                          • Pixels along the torus surface are plotted at fixed-angle increments, simulating a solid shape.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                                          • Projection Simplification:<\/strong>\n
                                              \n
                                            • 3D projection onto the 2D screen involves scaling coordinates and depth buffering to manage overlapping points.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                                            • Surface Normal Calculation:<\/strong>\n
                                                \n
                                              • The direction perpendicular to the torus surface at each point is computed for illumination purposes.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                                              • Lighting Direction:<\/strong>\n
                                                  \n
                                                • A lighting direction is chosen to determine the shade of each pixel, affecting its appearance.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n

                                                  any fun codes suggestion?<\/h2>\n\n\n\n

                                                  Same, after writing this post, I didn’t understand a thing. But I hope you have fun feeling cool reading this! I only know donut in coding C, so please lemme know if there is any fun code math out there in the comment section.<\/p>\n","protected":false},"excerpt":{"rendered":"

                                                  When I thought of coding tutorial, I know I must a post on donut-shaped C code that generates a 3D spinning donut. It’s just so legendary that you have to know it. Although I’m good at math in highschool, I haven\u2019t touched math for the last 3 years. In this post, instead of bombing with […]<\/p>\n","protected":false},"author":13,"featured_media":300,"comment_status":"open","ping_status":"open","sticky":false,"template":"single-with-sidebar","format":"standard","meta":{"_crdt_document":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-228","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-tutorial"],"_links":{"self":[{"href":"https:\/\/croakthecode.tcu.edu\/nguyen\/wp-json\/wp\/v2\/posts\/228","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/croakthecode.tcu.edu\/nguyen\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/croakthecode.tcu.edu\/nguyen\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/croakthecode.tcu.edu\/nguyen\/wp-json\/wp\/v2\/users\/13"}],"replies":[{"embeddable":true,"href":"https:\/\/croakthecode.tcu.edu\/nguyen\/wp-json\/wp\/v2\/comments?post=228"}],"version-history":[{"count":0,"href":"https:\/\/croakthecode.tcu.edu\/nguyen\/wp-json\/wp\/v2\/posts\/228\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/croakthecode.tcu.edu\/nguyen\/wp-json\/wp\/v2\/media\/300"}],"wp:attachment":[{"href":"https:\/\/croakthecode.tcu.edu\/nguyen\/wp-json\/wp\/v2\/media?parent=228"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/croakthecode.tcu.edu\/nguyen\/wp-json\/wp\/v2\/categories?post=228"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/croakthecode.tcu.edu\/nguyen\/wp-json\/wp\/v2\/tags?post=228"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}