https://www.khanacademy.org/computing/pixar/sets/sets1/v/sets-1 2023-07-31T16:40:28.830178554Z 1. Coordinate plane Learn how Pixar uses geometric transformations to create movie scenes. Starting with large forms like walls and floors, animators add elements like furniture. These items are positioned, sized, and oriented using translation, scaling, and rotation operations. video https://cdn.kastatic.org/googleusercontent/bn_bI5PmpjoMc5p5VGEXKl-p5T8drqrkFKLQtx2nlvRnr4C3nRY_bNWCiHoYS1bf9GJzZDm8m_KlgxWCbCC9VvyHAw 1. Coordinate plane Learn how Pixar uses geometric transformations to create movie scenes. Starting with large forms like walls and floors, animators add elements like furniture. These items are positioned, sized, and oriented using translation, scaling, and rotation operations. https://cdn.kastatic.org/ka-youtube-converted/Z_m9_WOdZ_k.mp4/Z_m9_WOdZ_k.mp4 104 Transformaciones geométricas https://www.khanacademy.org/math/cc-fifth-grade-math/imp-geometry-3/imp-intro-to-the-coordinate-plane/e/graphing_points 2026-04-01T22:33:24.722580916Z Graph points Plot a given point on the coordinate plane. Ben Eater exercise https://www.khanacademy.org/computing/pixar/sets/sets1/v/sets-2 2023-07-31T16:40:28.830178554Z 2. Translation Now we begin laying out our scene, starting with translation. We start by positioning an object at a reference point in the scene, and then add to its position to translate it to its desired position. Every object's placement tells a story! video https://cdn.kastatic.org/googleusercontent/15jNWLkbcRpT0PhSYGwJno0W2EWQOvmU12e8cQG_F7tur7XpYbXFricPstx5TU-g_Bjbp69yqsU1hWZMzQ0wFXQe 2. Translation Now we begin laying out our scene, starting with translation. We start by positioning an object at a reference point in the scene, and then add to its position to translate it to its desired position. Every object's placement tells a story! https://cdn.kastatic.org/ka-youtube-converted/C_HcAE8IUqQ.mp4/C_HcAE8IUqQ.mp4 165 Transformaciones geométricas https://www.khanacademy.org/computing/pixar/sets/sets1/a/laying-out-a-scene-using-translation 2025-12-15T19:40:37.959418087Z Laying out a scene using translation article https://www.khanacademy.org/computing/pixar/sets/sets1/v/set-3 2023-07-31T16:40:28.830178554Z 3. Scaling Scaling changes an object's size by multiplying its coordinates, while translation moves it to a new location. We scale an object so it fits the scene! video https://cdn.kastatic.org/googleusercontent/50CU5el3DeAG8rJ_zQzzgJnwr0cFQlqoRoHI2W3TduLXmv5oHwUQod-SlVItHA3gS2USzGORHdGm1GGjP2yz3kg 3. Scaling Scaling changes an object's size by multiplying its coordinates, while translation moves it to a new location. We scale an object so it fits the scene! https://cdn.kastatic.org/ka-youtube-converted/T_NdGA0CcXI.mp4/T_NdGA0CcXI.mp4 125 Transformaciones geométricas https://www.khanacademy.org/computing/pixar/sets/sets1/v/sets-4 2023-07-31T16:40:28.830178554Z 4. Commutativity We need to be careful with the order of scaling and translation. But why? First, we move an object 5 steps to the right and 3 steps up. Then, we make the object twice as big. But, if we first make the object big and then move it, we end up in a different place! This means the order of doing things matters. When the order doesn't matter, we call it "commutative". When the order does matter, we call it "non-commutative". video https://cdn.kastatic.org/googleusercontent/s9aKaZ_RvnBR02oX6Zn1iCYDWFCbyvQ6O0eq02GOqchdK9HMB5S9l7liez7e8IAqckh0iPSp0zm9BS-rZY3y9AqY 4. Commutativity We need to be careful with the order of scaling and translation. But why? First, we move an object 5 steps to the right and 3 steps up. Then, we make the object twice as big. But, if we first make the object big and then move it, we end up in a different place! This means the order of doing things matters. When the order doesn't matter, we call it "commutative". When the order does matter, we call it "non-commutative". https://cdn.kastatic.org/ka-youtube-converted/wbksgG0dQoE.mp4/wbksgG0dQoE.mp4 100 Transformaciones geométricas https://www.khanacademy.org/computing/pixar/sets/sets1/e/commutative-and-non-commutative-transformations 2021-06-05T01:55:17Z Commutative and non-commutative transformations Understand which sets of transformations are commutative. Peter Collingridge exercise https://www.khanacademy.org/computing/pixar/sets/sets1/v/sets-5 2023-07-31T16:40:28.830178554Z 5. Rotation Rotation turns objects in the scene around. To create a scene, we use all three transformations: scaling (adjusting size), rotation (turning objects), and translation (moving objects). The sequence of these operations is crucial, as changing the order can lead to different results! video https://cdn.kastatic.org/googleusercontent/DsCtuaiVJ8y0dXAZfJeGHex9kBXMEoWUxUn2tJU-rSN48duFAcAF9lf8j_Q69PudK-prnxcJaWtEnLF0D99DP6j4uQ 5. Rotation Rotation turns objects in the scene around. To create a scene, we use all three transformations: scaling (adjusting size), rotation (turning objects), and translation (moving objects). The sequence of these operations is crucial, as changing the order can lead to different results! https://cdn.kastatic.org/ka-youtube-converted/59XYyyia1Fk.mp4/59XYyyia1Fk.mp4 115 Transformaciones geométricas https://www.khanacademy.org/computing/pixar/sets/sets1/a/rotating-items-in-a-scene 2025-12-15T19:40:37.959418087Z Finish your scene! article https://www.khanacademy.org/computing/pixar/sets/sets1/v/sets-6 2023-07-31T16:40:28.830178554Z 6. Composite transformations We demonstrate, using algebra, why the order of two transformations - like scaling and translating - results in different outcomes. A combination of two or more transformations is called a composite transformation. video https://cdn.kastatic.org/googleusercontent/1mJHCKwabeMtdBgZU1GJngfLLqfc3cI8EkfLH0rIVRvzhp02ehlE2awZgbhgHEf3xgFmwxL6Kuu6uet1kjcMdg 6. Composite transformations We demonstrate, using algebra, why the order of two transformations - like scaling and translating - results in different outcomes. A combination of two or more transformations is called a composite transformation. https://cdn.kastatic.org/ka-youtube-converted/RqUfUxaY6HU.mp4/RqUfUxaY6HU.mp4 185 Transformaciones geométricas https://www.khanacademy.org/computing/pixar/sets/sets1/e/combining-transformations 2021-06-05T01:49:28Z Composite transformations Understand the result of combining different transformations Peter Collingridge exercise