Add XMMatrixPerspectiveFovInfiniteReverseZLH/RH - #334
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Implements infinite reversed-z perspective projection matrices, resolving issue microsoft#158. These functions complement the existing XMMatrixPerspectiveFovLH/RH pair for the increasingly common rendering technique of reversed-z with an infinite far plane, which provides optimal floating-point depth precision and eliminates Z-fighting at large distances. The algebraic derivation takes the limit of XMMatrixPerspectiveFovLH as FarZ -> +infinity. Using the standard row-major DX NDC mapping: NDC_z = M22 + M32 / z Setting NDC_z(NearZ) = 1 and NDC_z(inf) = 0 gives: M22 = 0, M32 = NearZ (LH) M22 = 0, M32 = -NearZ (RH) All three code paths are implemented: - Scalar (_XM_NO_INTRINSICS_) - ARM NEON (_XM_ARM_NEON_INTRINSICS_) - SSE/AVX (_XM_SSE_INTRINSICS_) Unlike substituting infinity into the existing FovLH/RH functions, these functions produce well-defined, NaN-free results.
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Collaborator
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If you have example test code for this, please attach and I can integrate it into https://github.com/walbourn/directxmathtest |
Author
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I realized my earlier test code was written as a standalone executable rather than following the math3 harness format. I've corrected it. The attached file uses the HRESULT TestNNN(LogProxy* pLog) pattern and printe/printi from math3.h. Please assign the appropriate test numbers. Click to expand test code (XMMatrixInfiniteReverseZ.cpp)//-------------------------------------------------------------------------------------
// XMMatrixInfiniteReverseZ.cpp - DirectXMath Test Suite
//
// Tests for XMMatrixPerspectiveFovInfiniteReverseZLH and
// XMMatrixPerspectiveFovInfiniteReverseZRH
//
// Resolves: https://github.com/microsoft/DirectXMath/issues/158
//
// Copyright (c) Microsoft Corporation.
// Licensed under the MIT License.
//
// https://go.microsoft.com/fwlink/?LinkID=615560
//-------------------------------------------------------------------------------------
//
// NOTE TO MAINTAINER:
// Please assign test numbers and register these functions in math3.cpp /
// AssignTests(). Two functions are provided:
// TestNNN -> XMMatrixPerspectiveFovInfiniteReverseZLH
// TestNNN1 -> XMMatrixPerspectiveFovInfiniteReverseZRH
//
#include "math3.h"
#include <cmath>
#include <limits>
using namespace DirectX;
// Helper: compute NDC z from a stored 4x4 matrix and a view-space z value.
// NDC_z = (M[2][2]*z + M[3][2]) / (M[2][3]*z + M[3][3])
// Uses XMFLOAT4X4 row-major element names (_33 = row2,col2, etc.)
static float ComputeNDCz(const XMFLOAT4X4& m, float z)
{
float num = m._33 * z + m._43;
float den = m._34 * z + m._44;
return num / den;
}
//------------------------------------------------------------------------------
// TestNNN - XMMatrixPerspectiveFovInfiniteReverseZLH
//
// Verifies the left-handed infinite reversed-Z projection matrix:
// [xScale 0 0 0]
// [0 yScale 0 0]
// [0 0 0 1]
// [0 0 zNear 0]
//
// Key properties:
// M[2][2] == 0 (no finite far plane term)
// M[3][2] == NearZ (reversed-Z: near maps to NDC 1.0)
// M[2][3] == 1 (left-handed)
// NDC_z(NearZ) == 1.0
// NDC_z(inf) ~= 0.0
//------------------------------------------------------------------------------
HRESULT TestNNN(LogProxy* pLog)
{
// XMMatrixPerspectiveFovInfiniteReverseZLH
HRESULT ret = S_OK;
const float fovY = XM_PIDIV4; // 45 degrees
const float aspect = 16.0f / 9.0f; // 16:9 widescreen
const float nearZ = 0.1f;
XMMATRIX M = XMMatrixPerspectiveFovInfiniteReverseZLH(fovY, aspect, nearZ);
XMFLOAT4X4 f;
XMStoreFloat4x4(&f, M);
// --- Structure checks ---
// M[2][2] must be exactly 0 (the infinite far-plane term cancels out)
if (f._33 != 0.0f)
{
printe("%s: LH M[2][2] expected 0.0, got %f\n", TestName, f._33);
ret = MATH_FAIL;
}
else
{
printi("%s: LH M[2][2]==0 OK\n", TestName);
}
// M[3][2] must equal NearZ (reversed-Z: near plane clips to NDC 1.0)
if (f._43 != nearZ)
{
printe("%s: LH M[3][2] expected %f, got %f\n", TestName, nearZ, f._43);
ret = MATH_FAIL;
}
else
{
printi("%s: LH M[3][2]==NearZ OK\n", TestName);
}
// M[2][3] must be 1.0 for a left-handed projection
if (f._34 != 1.0f)
{
printe("%s: LH M[2][3] expected 1.0, got %f\n", TestName, f._34);
ret = MATH_FAIL;
}
else
{
printi("%s: LH M[2][3]==1 OK\n", TestName);
}
// M[3][3] must be 0.0
if (f._44 != 0.0f)
{
printe("%s: LH M[3][3] expected 0.0, got %f\n", TestName, f._44);
ret = MATH_FAIL;
}
else
{
printi("%s: LH M[3][3]==0 OK\n", TestName);
}
// X and Y scale must be positive
if (f._11 <= 0.0f || f._22 <= 0.0f)
{
printe("%s: LH scale must be positive: _11=%f _22=%f\n", TestName, f._11, f._22);
ret = MATH_FAIL;
}
else
{
printi("%s: LH XY scale positive OK\n", TestName);
}
// Off-diagonal elements must be zero
if (f._12 != 0.f || f._13 != 0.f || f._14 != 0.f ||
f._21 != 0.f || f._23 != 0.f || f._24 != 0.f ||
f._31 != 0.f || f._32 != 0.f ||
f._41 != 0.f || f._42 != 0.f)
{
printe("%s: LH off-diagonal elements are not zero\n", TestName);
ret = MATH_FAIL;
}
else
{
printi("%s: LH off-diagonal zeros OK\n", TestName);
}
// --- Depth mapping checks ---
// At the near plane, NDC z must be exactly 1.0 (reversed-Z maps near to 1)
{
float ndc = ComputeNDCz(f, nearZ);
if (fabsf(ndc - 1.0f) > 1e-5f)
{
printe("%s: LH NDC_z(NearZ=%.2f) expected 1.0, got %f\n", TestName, nearZ, ndc);
ret = MATH_FAIL;
}
else
{
printi("%s: LH NDC_z(NearZ)==1.0 OK\n", TestName);
}
}
// At z approaching infinity, NDC z must approach 0.0
{
float ndc = ComputeNDCz(f, 1e9f);
if (fabsf(ndc) > 1e-5f)
{
printe("%s: LH NDC_z(inf) expected ~0.0, got %f\n", TestName, ndc);
ret = MATH_FAIL;
}
else
{
printi("%s: LH NDC_z(inf)~=0 OK\n", TestName);
}
}
return ret;
}
//------------------------------------------------------------------------------
// TestNNN1 - XMMatrixPerspectiveFovInfiniteReverseZRH
//
// Verifies the right-handed infinite reversed-Z projection matrix:
// [xScale 0 0 0 ]
// [0 yScale 0 0 ]
// [0 0 0 -1 ]
// [0 0 -zNear 0]
//
// Key properties:
// M[2][2] == 0 (no finite far plane term)
// M[3][2] == -NearZ (reversed-Z, right-handed)
// M[2][3] == -1 (right-handed)
// NDC_z(NearZ) == 1.0
// NDC_z(inf) ~= 0.0
// X/Y scaling matches the LH variant for same FOV+aspect
//
// Also confirms that the naive workaround (passing INFINITY to the existing
// XMMatrixPerspectiveFovLH) produces NaN, justifying these new functions.
//------------------------------------------------------------------------------
HRESULT TestNNN1(LogProxy* pLog)
{
// XMMatrixPerspectiveFovInfiniteReverseZRH
HRESULT ret = S_OK;
const float fovY = XM_PIDIV4;
const float aspect = 16.0f / 9.0f;
const float nearZ = 0.1f;
XMMATRIX M = XMMatrixPerspectiveFovInfiniteReverseZRH(fovY, aspect, nearZ);
XMFLOAT4X4 f;
XMStoreFloat4x4(&f, M);
// --- Structure checks ---
if (f._33 != 0.0f)
{
printe("%s: RH M[2][2] expected 0.0, got %f\n", TestName, f._33);
ret = MATH_FAIL;
}
else
{
printi("%s: RH M[2][2]==0 OK\n", TestName);
}
if (f._43 != -nearZ)
{
printe("%s: RH M[3][2] expected %f (-NearZ), got %f\n", TestName, -nearZ, f._43);
ret = MATH_FAIL;
}
else
{
printi("%s: RH M[3][2]==-NearZ OK\n", TestName);
}
if (f._34 != -1.0f)
{
printe("%s: RH M[2][3] expected -1.0, got %f\n", TestName, f._34);
ret = MATH_FAIL;
}
else
{
printi("%s: RH M[2][3]==-1 OK\n", TestName);
}
if (f._44 != 0.0f)
{
printe("%s: RH M[3][3] expected 0.0, got %f\n", TestName, f._44);
ret = MATH_FAIL;
}
else
{
printi("%s: RH M[3][3]==0 OK\n", TestName);
}
if (f._11 <= 0.0f || f._22 <= 0.0f)
{
printe("%s: RH scale must be positive: _11=%f _22=%f\n", TestName, f._11, f._22);
ret = MATH_FAIL;
}
else
{
printi("%s: RH XY scale positive OK\n", TestName);
}
if (f._12 != 0.f || f._13 != 0.f || f._14 != 0.f ||
f._21 != 0.f || f._23 != 0.f || f._24 != 0.f ||
f._31 != 0.f || f._32 != 0.f ||
f._41 != 0.f || f._42 != 0.f)
{
printe("%s: RH off-diagonal elements are not zero\n", TestName);
ret = MATH_FAIL;
}
else
{
printi("%s: RH off-diagonal zeros OK\n", TestName);
}
// --- Depth mapping checks ---
// At near plane (RH looks down -Z, so z = nearZ positive here for formula)
{
float ndc = ComputeNDCz(f, nearZ);
if (fabsf(ndc - 1.0f) > 1e-5f)
{
printe("%s: RH NDC_z(NearZ=%.2f) expected 1.0, got %f\n", TestName, nearZ, ndc);
ret = MATH_FAIL;
}
else
{
printi("%s: RH NDC_z(NearZ)==1.0 OK\n", TestName);
}
}
// At z approaching -infinity (RH far), NDC z must approach 0.0
{
float ndc = ComputeNDCz(f, -1e9f);
if (fabsf(ndc) > 1e-5f)
{
printe("%s: RH NDC_z(-inf) expected ~0.0, got %f\n", TestName, ndc);
ret = MATH_FAIL;
}
else
{
printi("%s: RH NDC_z(-inf)~=0 OK\n", TestName);
}
}
// --- LH / RH consistency: same FOV+aspect must produce same X/Y scale ---
{
XMMATRIX lhM = XMMatrixPerspectiveFovInfiniteReverseZLH(fovY, aspect, nearZ);
XMFLOAT4X4 lhF;
XMStoreFloat4x4(&lhF, lhM);
if (lhF._11 != f._11 || lhF._22 != f._22)
{
printe("%s: LH/RH X scale mismatch: LH=%f RH=%f\n", TestName, lhF._11, f._11);
printe("%s: LH/RH Y scale mismatch: LH=%f RH=%f\n", TestName, lhF._22, f._22);
ret = MATH_FAIL;
}
else
{
printi("%s: LH/RH XY scale match OK\n", TestName);
}
}
// --- Confirm the naive workaround produces NaN (justifies these functions) ---
// Passing INFINITY as FarZ to the existing function computes 0 * INFINITY = NaN.
{
const float inf = std::numeric_limits<float>::infinity();
XMMATRIX broken = XMMatrixPerspectiveFovLH(fovY, aspect, nearZ, inf);
XMFLOAT4X4 b;
XMStoreFloat4x4(&b, broken);
if (std::isnan(b._43) || std::isnan(b._33))
{
printi("%s: naive INFINITY workaround produces NaN as expected OK\n", TestName);
}
else
{
// Not a failure of the new functions; just informational for this platform.
printi("%s: note - naive INFINITY workaround did not produce NaN on this platform\n", TestName);
}
}
return ret;
} |
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Summary
This PR adds dedicated functions for infinite reversed-Z perspective projections, addressing Issue #158.
Passing
INFINITYas the far plane to the existingXMMatrixPerspectiveFovLH/XMMatrixPerspectiveFovRHfunctions is not sufficient because the internal calculations contain floating-point operations such as0 * infinity, which result inNaNvalues.This change derives the limiting form of the perspective projection matrix when the far plane approaches infinity and introduces:
XMMatrixPerspectiveFovInfiniteReverseZLHXMMatrixPerspectiveFovInfiniteReverseZRHThe generated matrices match the layout discussed in Issue #158:
Changes
Added infinite reversed-Z perspective projection functions for:
_XM_NO_INTRINSICS_)_XM_ARM_NEON_INTRINSICS_)_XM_SSE_INTRINSICS_)Added local validation tests covering:
The existing implementation was also tested with
INFINITYas the far plane and confirmed to produceNaNvalues.Screenshots: