Computer Graphics: Difference between revisions

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[https://www.scratchapixel.com/lessons/3d-basic-rendering/perspective-and-orthographic-projection-matrix/building-basic-perspective-projection-matrix https://www.scratchapixel.com/lessons/3d-basic-rendering/perspective-and-orthographic-projection-matrix/building-basic-perspective-projection-matrix]

The projection matrix applies a perspective projection based on the field of view of the camera. This is done dividing the x,y view coordinates by the z-coordinate so that further object appear closer to the center. Note that the output is typically in normalized device coordinates <math>[-1, 1]\times[-1, 1]</math> rather than image coordinates <math>[0, W] \times [0, H]</math>.

https://www.songho.ca/opengl/gl_projectionmatrix.html

The projection matrix applies a perspective projection based on the field of view of the camera. This is done dividing the x,y view coordinates by the z-coordinate so that further object appear closer to the center. Note that the output is typically in normalized device coordinates (NDC) <math>[-1, 1]\times[-1, 1]</math> rather than image coordinates <math>{0, ..., W-1} \times {0, ..., H-1}</math>. Additionally, in NDC, the y-coordinate typically points upwards unlike image coordinates.

The Z-coordinate in the projection matrix represents a remapped version of the z-depth, i.e. depth along the camera forward axis. In OpenGL, this maps z=-f to 1 and z=-n to -1 where -z is forward.

Notes: In computer vision, this is analogous to the calibration matrix <math>K</math>.

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 [https://www.scratchapixel.com/lessons/3d-basic-rendering/perspective-and-orthographic-projection-matrix/building-basic-perspective-projection-matrix https://www.scratchapixel.com/lessons/3d-basic-rendering/perspective-and-orthographic-projection-matrix/building-basic-perspective-projection-matrix]
-The projection matrix applies a perspective projection based on the field of view of the camera. This is done dividing the x,y view coordinates by the z-coordinate so that further object appear closer to the center. Note that the output is typically in normalized device coordinates <math>[-1, 1]\times[-1, 1]</math> rather than image coordinates <math>[0, W] \times [0, H]</math>.
+https://www.songho.ca/opengl/gl_projectionmatrix.html
+The projection matrix applies a perspective projection based on the field of view of the camera. This is done dividing the x,y view coordinates by the z-coordinate so that further object appear closer to the center. Note that the output is typically in normalized device coordinates (NDC) <math>[-1, 1]\times[-1, 1]</math> rather than image coordinates <math>{0, ..., W-1} \times {0, ..., H-1}</math>. Additionally, in NDC, the y-coordinate typically points upwards unlike image coordinates.
+The Z-coordinate in the projection matrix represents a remapped version of the z-depth, i.e. depth along the camera forward axis. In OpenGL, this maps z=-f to 1 and z=-n to -1 where -z is forward.
 Notes: In computer vision, this is analogous to the calibration matrix <math>K</math>.