60 lines
1.6 KiB
C++
60 lines
1.6 KiB
C++
#pragma once
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#include <math/mat4.hpp>
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namespace lt::math {
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/**
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* let...
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* a = h / w ==> for aspect ratio adjustment
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* f = 1 / tan(fov / 2) ==> for field of view
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*
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* zdiff = zfar-znear
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* A = (zfar / zdiff) - (zfar / zdiff * znear) ==> for normalization
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*
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* given a 3d position vector xyz, we need to do the following operations to achieve
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* perspective projection:
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* x afx
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* y --> fy
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* z Az - Aznear
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*
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* such calculation can be embdedded in a matrix as:
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* [x] [y] [z] [w]
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*
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* | af | 0 | 0 | 0 |
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* ----------------------------------
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* | 0 | f | 0 | 0 |
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* ----------------------------------
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* | 0 | 0 | A | A*znear|
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* ----------------------------------
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* | 0 | 0 | 1 | 0 |
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*
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* the 1 at [z][3] is to save the Z axis into the resulting W for perspective division.
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*
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* @ref Thanks to pikuma for explaining the math behind this:
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* https://www.youtube.com/watch?v=EqNcqBdrNyI
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*/
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template<typename T>
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constexpr auto perspective(T field_of_view, T aspect_ratio, T z_near, T z_far)
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{
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const T half_fov_tan = std::tan(field_of_view / static_cast<T>(2));
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auto result = mat4_impl<T>::identity();
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result[0][0] = T { 1 } / (aspect_ratio * half_fov_tan);
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//
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result[1][1] = T { 1 } / (half_fov_tan);
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//
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// result[2][2] = -(z_far + z_near) / (z_far - z_near);
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//
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result[2][2] = z_far / (z_far - z_near);
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//
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result[2][3] = -T { 1 };
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//
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// result[3][2] = -(T { 2 } * z_far * z_near) / (z_far - z_near);
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result[3][2] = -(z_far * z_near) / (z_far - z_near);
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//
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return result;
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}
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} // namespace lt::math
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