René's URL Explorer Experiment

{"@context":"https://schema.org","@type":"DiscussionForumPosting","headline":"[ENH]: Specify a custom focal length / FOV for the 3d camera","articleBody":"### Problem\r\n\r\nI'd like to be able to recreate the perspective-warping effects of changing focal length / FOV of a physical camera in matplotlib, for more fine-tuned camera control and for replicating real-world cameras in software.\r\n\r\n### Proposed solution\r\n\r\nFrom [this slide deck](http://www.terathon.com/gdc07_lengyel.pdf), we see how to generate a projection matrix: \r\n![image](https://user-images.githubusercontent.com/14363975/147036962-ae29a06c-02c0-48e7-b1f6-f789ba4bddc9.png)\r\n\r\n[This page has a nice derivation of the matrix](https://www.scratchapixel.com/lessons/3d-basic-rendering/perspective-and-orthographic-projection-matrix/opengl-perspective-projection-matrix).\r\n\r\nThe persp_transformation function in [/lib/mpl_toolkits/mplot3d/proj3d.py](https://github.com/matplotlib/matplotlib/blob/main/lib/mpl_toolkits/mplot3d/proj3d.py) implements this for a fixed focal distance of 1 (equivalent to a FOV of 90 deg):\r\n```\r\ndef persp_transformation(zfront, zback):\r\n    a = (zfront+zback)/(zfront-zback)\r\n    b = -2*(zfront*zback)/(zfront-zback)\r\n    return np.array([[1, 0, 0, 0],\r\n                     [0, 1, 0, 0],\r\n                     [0, 0, a, b],\r\n                     [0, 0, -1, 0]])\r\n```\r\n\r\nIt should not be too hard to update this function to take in a focal length. I think the biggest question is the user interface. ~~The `focal_length` can be taken as fundamental and the current `proj_type` arguments to the Axes3D constructor can be mapped to `focal_length = 1` for `proj_type == 'persp'`. To specify a custom focal length however, what should the user input?~~ \r\n\r\nEdit: I think the easiest thing would be a default `focal_length = None` argument, which can be set by the user but otherwise gets set to 1 if  `proj_type == 'persp'`.","author":{"url":"https://github.com/scottshambaugh","@type":"Person","name":"scottshambaugh"},"datePublished":"2021-12-22T05:00:56.000Z","interactionStatistic":{"@type":"InteractionCounter","interactionType":"https://schema.org/CommentAction","userInteractionCount":6},"url":"https://github.com/22035/matplotlib/issues/22035"}