a/math: Add projection matrix making function

src/xrt/auxiliary/math/CMakeLists.txt

@@ -28,6 +28,7 @@ add_library(
 	m_lowpass_integer.hpp
 	m_matrix_2x2.h
 	m_matrix_4x4_f64.h
+	m_matrix_projection.cpp
 	m_optics.c
 	m_permutation.c
 	m_permutation.h

src/xrt/auxiliary/math/m_api.h

@@ -655,6 +655,19 @@ math_matrix_4x4_inverse_view_projection(const struct xrt_matrix_4x4 *view,
                                         const struct xrt_matrix_4x4 *projection,
                                         struct xrt_matrix_4x4 *result);
 
+/*!
+ * Compute a projection matrix with settings for Vulkan, it will also have it's
+ * far plane at infinite and the NDC depth will be reversed.
+ *
+ * @relates xrt_matrix_4x4
+ * @ingroup aux_math
+ */
+void
+math_matrix_4x4_projection_vulkan_infinite_reverse(const struct xrt_fov *fov,
+                                                   float near_plane,
+                                                   struct xrt_matrix_4x4 *result);
+
+
 /*
  *
  * Pose functions.

src/xrt/auxiliary/math/m_matrix_projection.cpp

@@ -0,0 +1,81 @@
+// Copyright 2019-2023, Collabora, Ltd.
+// SPDX-License-Identifier: BSL-1.0
+/*!
+ * @file
+ * @brief  Matrix function for creating projection matrices.
+ * @author Jakob Bornecrantz <jakob@collabora.com>
+ * @ingroup aux_math
+ */
+
+#include "m_mathinclude.h"
+#include "xrt/xrt_defines.h"
+
+
+/*
+ *
+ * Helpers.
+ *
+ */
+
+template <typename Scalar, typename ResultType>
+void
+calc_vulkan_projection_infinite_reverse(const xrt_fov &fov, Scalar near_plane, ResultType &result)
+{
+	const Scalar tan_left = static_cast<Scalar>(tan(fov.angle_left));
+	const Scalar tan_right = static_cast<Scalar>(tan(fov.angle_right));
+
+	const Scalar tan_down = static_cast<Scalar>(tan(fov.angle_down));
+	const Scalar tan_up = static_cast<Scalar>(tan(fov.angle_up));
+
+	// This is here for clarity.
+	const bool vulkan_projection_space_y = true;
+
+	const Scalar tan_width = tan_right - tan_left;
+	const Scalar tan_height = vulkan_projection_space_y  // Projection space y direction:
+	                              ? (tan_down - tan_up)  // Vulkan Y down
+	                              : (tan_up - tan_down); // OpenGL Y up
+
+	const Scalar a11 = 2 / tan_width;
+	const Scalar a22 = 2 / tan_height;
+
+	const Scalar a31 = (tan_right + tan_left) / tan_width;
+	const Scalar a32 = (tan_up + tan_down) / tan_height;
+
+
+	/*
+	 * Vulkan's Z clip space is [0 .. 1] (OpenGL [-1 .. 0 .. 1]).
+	 * We are using reverse depth for better floating value.
+	 *  - Near is 1
+	 *  - Far is 0 (infinite)
+	 *
+	 * https://vincent-p.github.io/posts/vulkan_perspective_matrix/
+	 */
+
+	const Scalar a33 = 0; // vulkan = 0, opengl = -1
+	const Scalar a34 = -1;
+	const Scalar a43 = near_plane; // Reverse depth and half vs opengl, `-2 * near_plane`.
+
+	// clang-format off
+	result = ResultType({
+		a11,   0,   0,   0,
+		  0, a22,   0,   0,
+		a31, a32, a33, a34,
+		  0,   0, a43,   0,
+	});
+	// clang-format on
+}
+
+
+/*
+ *
+ * 'Exported' functions.
+ *
+ */
+
+extern "C" void
+math_matrix_4x4_projection_vulkan_infinite_reverse(const struct xrt_fov *fov,
+                                                   float near_plane,
+                                                   struct xrt_matrix_4x4 *result)
+{
+	calc_vulkan_projection_infinite_reverse<float, xrt_matrix_4x4>(*fov, near_plane, *result);
+}