ppsspp/Common/VR/VRMath.cpp
2022-10-18 10:35:42 +02:00

419 lines
13 KiB
C++

#define _USE_MATH_DEFINES
#include <cmath>
#include "VRMath.h"
float ToDegrees(float rad) {
return (float)(rad / M_PI * 180.0f);
}
float ToRadians(float deg) {
return (float)(deg * M_PI / 180.0f);
}
/*
================================================================================
ovrMatrix4f
================================================================================
*/
float ovrMatrix4f_Minor(const ovrMatrix4f* m, int r0, int r1, int r2, int c0, int c1, int c2) {
return m->M[r0][c0] * (m->M[r1][c1] * m->M[r2][c2] - m->M[r2][c1] * m->M[r1][c2]) -
m->M[r0][c1] * (m->M[r1][c0] * m->M[r2][c2] - m->M[r2][c0] * m->M[r1][c2]) +
m->M[r0][c2] * (m->M[r1][c0] * m->M[r2][c1] - m->M[r2][c0] * m->M[r1][c1]);
}
ovrMatrix4f ovrMatrix4f_CreateFromQuaternion(const XrQuaternionf* q) {
const float ww = q->w * q->w;
const float xx = q->x * q->x;
const float yy = q->y * q->y;
const float zz = q->z * q->z;
ovrMatrix4f out;
out.M[0][0] = ww + xx - yy - zz;
out.M[0][1] = 2 * (q->x * q->y - q->w * q->z);
out.M[0][2] = 2 * (q->x * q->z + q->w * q->y);
out.M[0][3] = 0;
out.M[1][0] = 2 * (q->x * q->y + q->w * q->z);
out.M[1][1] = ww - xx + yy - zz;
out.M[1][2] = 2 * (q->y * q->z - q->w * q->x);
out.M[1][3] = 0;
out.M[2][0] = 2 * (q->x * q->z - q->w * q->y);
out.M[2][1] = 2 * (q->y * q->z + q->w * q->x);
out.M[2][2] = ww - xx - yy + zz;
out.M[2][3] = 0;
out.M[3][0] = 0;
out.M[3][1] = 0;
out.M[3][2] = 0;
out.M[3][3] = 1;
return out;
}
ovrMatrix4f ovrMatrix4f_CreateProjectionFov(
const float angleLeft,
const float angleRight,
const float angleUp,
const float angleDown,
const float nearZ,
const float farZ) {
const float tanAngleLeft = tanf(angleLeft);
const float tanAngleRight = tanf(angleRight);
const float tanAngleDown = tanf(angleDown);
const float tanAngleUp = tanf(angleUp);
const float tanAngleWidth = tanAngleRight - tanAngleLeft;
// Set to tanAngleDown - tanAngleUp for a clip space with positive Y
// down (Vulkan). Set to tanAngleUp - tanAngleDown for a clip space with
// positive Y up (OpenGL / D3D / Metal).
const float tanAngleHeight = tanAngleUp - tanAngleDown;
// Set to nearZ for a [-1,1] Z clip space (OpenGL / OpenGL ES).
// Set to zero for a [0,1] Z clip space (Vulkan / D3D / Metal).
const float offsetZ = nearZ;
ovrMatrix4f result;
if (farZ <= nearZ) {
// place the far plane at infinity
result.M[0][0] = 2 / tanAngleWidth;
result.M[0][1] = 0;
result.M[0][2] = (tanAngleRight + tanAngleLeft) / tanAngleWidth;
result.M[0][3] = 0;
result.M[1][0] = 0;
result.M[1][1] = 2 / tanAngleHeight;
result.M[1][2] = (tanAngleUp + tanAngleDown) / tanAngleHeight;
result.M[1][3] = 0;
result.M[2][0] = 0;
result.M[2][1] = 0;
result.M[2][2] = -1;
result.M[2][3] = -(nearZ + offsetZ);
result.M[3][0] = 0;
result.M[3][1] = 0;
result.M[3][2] = -1;
result.M[3][3] = 0;
} else {
// normal projection
result.M[0][0] = 2 / tanAngleWidth;
result.M[0][1] = 0;
result.M[0][2] = (tanAngleRight + tanAngleLeft) / tanAngleWidth;
result.M[0][3] = 0;
result.M[1][0] = 0;
result.M[1][1] = 2 / tanAngleHeight;
result.M[1][2] = (tanAngleUp + tanAngleDown) / tanAngleHeight;
result.M[1][3] = 0;
result.M[2][0] = 0;
result.M[2][1] = 0;
result.M[2][2] = -(farZ + offsetZ) / (farZ - nearZ);
result.M[2][3] = -(farZ * (nearZ + offsetZ)) / (farZ - nearZ);
result.M[3][0] = 0;
result.M[3][1] = 0;
result.M[3][2] = -1;
result.M[3][3] = 0;
}
return result;
}
ovrMatrix4f ovrMatrix4f_CreateRotation(const float radiansX, const float radiansY, const float radiansZ) {
const float sinX = sinf(radiansX);
const float cosX = cosf(radiansX);
const ovrMatrix4f rotationX = {
{{1, 0, 0, 0}, {0, cosX, -sinX, 0}, {0, sinX, cosX, 0}, {0, 0, 0, 1}}};
const float sinY = sinf(radiansY);
const float cosY = cosf(radiansY);
const ovrMatrix4f rotationY = {
{{cosY, 0, sinY, 0}, {0, 1, 0, 0}, {-sinY, 0, cosY, 0}, {0, 0, 0, 1}}};
const float sinZ = sinf(radiansZ);
const float cosZ = cosf(radiansZ);
const ovrMatrix4f rotationZ = {
{{cosZ, -sinZ, 0, 0}, {sinZ, cosZ, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}}};
const ovrMatrix4f rotationXY = ovrMatrix4f_Multiply(&rotationY, &rotationX);
return ovrMatrix4f_Multiply(&rotationZ, &rotationXY);
}
ovrMatrix4f ovrMatrix4f_Inverse(const ovrMatrix4f* m) {
const float rcpDet = 1.0f /
(m->M[0][0] * ovrMatrix4f_Minor(m, 1, 2, 3, 1, 2, 3) -
m->M[0][1] * ovrMatrix4f_Minor(m, 1, 2, 3, 0, 2, 3) +
m->M[0][2] * ovrMatrix4f_Minor(m, 1, 2, 3, 0, 1, 3) -
m->M[0][3] * ovrMatrix4f_Minor(m, 1, 2, 3, 0, 1, 2));
ovrMatrix4f out;
out.M[0][0] = ovrMatrix4f_Minor(m, 1, 2, 3, 1, 2, 3) * rcpDet;
out.M[0][1] = -ovrMatrix4f_Minor(m, 0, 2, 3, 1, 2, 3) * rcpDet;
out.M[0][2] = ovrMatrix4f_Minor(m, 0, 1, 3, 1, 2, 3) * rcpDet;
out.M[0][3] = -ovrMatrix4f_Minor(m, 0, 1, 2, 1, 2, 3) * rcpDet;
out.M[1][0] = -ovrMatrix4f_Minor(m, 1, 2, 3, 0, 2, 3) * rcpDet;
out.M[1][1] = ovrMatrix4f_Minor(m, 0, 2, 3, 0, 2, 3) * rcpDet;
out.M[1][2] = -ovrMatrix4f_Minor(m, 0, 1, 3, 0, 2, 3) * rcpDet;
out.M[1][3] = ovrMatrix4f_Minor(m, 0, 1, 2, 0, 2, 3) * rcpDet;
out.M[2][0] = ovrMatrix4f_Minor(m, 1, 2, 3, 0, 1, 3) * rcpDet;
out.M[2][1] = -ovrMatrix4f_Minor(m, 0, 2, 3, 0, 1, 3) * rcpDet;
out.M[2][2] = ovrMatrix4f_Minor(m, 0, 1, 3, 0, 1, 3) * rcpDet;
out.M[2][3] = -ovrMatrix4f_Minor(m, 0, 1, 2, 0, 1, 3) * rcpDet;
out.M[3][0] = -ovrMatrix4f_Minor(m, 1, 2, 3, 0, 1, 2) * rcpDet;
out.M[3][1] = ovrMatrix4f_Minor(m, 0, 2, 3, 0, 1, 2) * rcpDet;
out.M[3][2] = -ovrMatrix4f_Minor(m, 0, 1, 3, 0, 1, 2) * rcpDet;
out.M[3][3] = ovrMatrix4f_Minor(m, 0, 1, 2, 0, 1, 2) * rcpDet;
return out;
}
/// Use left-multiplication to accumulate transformations.
ovrMatrix4f ovrMatrix4f_Multiply(const ovrMatrix4f* a, const ovrMatrix4f* b) {
ovrMatrix4f out;
out.M[0][0] = a->M[0][0] * b->M[0][0] + a->M[0][1] * b->M[1][0] + a->M[0][2] * b->M[2][0] +
a->M[0][3] * b->M[3][0];
out.M[1][0] = a->M[1][0] * b->M[0][0] + a->M[1][1] * b->M[1][0] + a->M[1][2] * b->M[2][0] +
a->M[1][3] * b->M[3][0];
out.M[2][0] = a->M[2][0] * b->M[0][0] + a->M[2][1] * b->M[1][0] + a->M[2][2] * b->M[2][0] +
a->M[2][3] * b->M[3][0];
out.M[3][0] = a->M[3][0] * b->M[0][0] + a->M[3][1] * b->M[1][0] + a->M[3][2] * b->M[2][0] +
a->M[3][3] * b->M[3][0];
out.M[0][1] = a->M[0][0] * b->M[0][1] + a->M[0][1] * b->M[1][1] + a->M[0][2] * b->M[2][1] +
a->M[0][3] * b->M[3][1];
out.M[1][1] = a->M[1][0] * b->M[0][1] + a->M[1][1] * b->M[1][1] + a->M[1][2] * b->M[2][1] +
a->M[1][3] * b->M[3][1];
out.M[2][1] = a->M[2][0] * b->M[0][1] + a->M[2][1] * b->M[1][1] + a->M[2][2] * b->M[2][1] +
a->M[2][3] * b->M[3][1];
out.M[3][1] = a->M[3][0] * b->M[0][1] + a->M[3][1] * b->M[1][1] + a->M[3][2] * b->M[2][1] +
a->M[3][3] * b->M[3][1];
out.M[0][2] = a->M[0][0] * b->M[0][2] + a->M[0][1] * b->M[1][2] + a->M[0][2] * b->M[2][2] +
a->M[0][3] * b->M[3][2];
out.M[1][2] = a->M[1][0] * b->M[0][2] + a->M[1][1] * b->M[1][2] + a->M[1][2] * b->M[2][2] +
a->M[1][3] * b->M[3][2];
out.M[2][2] = a->M[2][0] * b->M[0][2] + a->M[2][1] * b->M[1][2] + a->M[2][2] * b->M[2][2] +
a->M[2][3] * b->M[3][2];
out.M[3][2] = a->M[3][0] * b->M[0][2] + a->M[3][1] * b->M[1][2] + a->M[3][2] * b->M[2][2] +
a->M[3][3] * b->M[3][2];
out.M[0][3] = a->M[0][0] * b->M[0][3] + a->M[0][1] * b->M[1][3] + a->M[0][2] * b->M[2][3] +
a->M[0][3] * b->M[3][3];
out.M[1][3] = a->M[1][0] * b->M[0][3] + a->M[1][1] * b->M[1][3] + a->M[1][2] * b->M[2][3] +
a->M[1][3] * b->M[3][3];
out.M[2][3] = a->M[2][0] * b->M[0][3] + a->M[2][1] * b->M[1][3] + a->M[2][2] * b->M[2][3] +
a->M[2][3] * b->M[3][3];
out.M[3][3] = a->M[3][0] * b->M[0][3] + a->M[3][1] * b->M[1][3] + a->M[3][2] * b->M[2][3] +
a->M[3][3] * b->M[3][3];
return out;
}
XrVector3f ovrMatrix4f_ToEulerAngles(const ovrMatrix4f* m) {
XrVector4f v1 = {0, 0, -1, 0};
XrVector4f v2 = {1, 0, 0, 0};
XrVector4f v3 = {0, 1, 0, 0};
XrVector4f forwardInVRSpace = XrVector4f_MultiplyMatrix4f(m, &v1);
XrVector4f rightInVRSpace = XrVector4f_MultiplyMatrix4f(m, &v2);
XrVector4f upInVRSpace = XrVector4f_MultiplyMatrix4f(m, &v3);
XrVector3f forward = {-forwardInVRSpace.z, -forwardInVRSpace.x, forwardInVRSpace.y};
XrVector3f right = {-rightInVRSpace.z, -rightInVRSpace.x, rightInVRSpace.y};
XrVector3f up = {-upInVRSpace.z, -upInVRSpace.x, upInVRSpace.y};
XrVector3f forwardNormal = XrVector3f_Normalized(forward);
XrVector3f rightNormal = XrVector3f_Normalized(right);
XrVector3f upNormal = XrVector3f_Normalized(up);
return XrVector3f_GetAnglesFromVectors(forwardNormal, rightNormal, upNormal);
}
/*
================================================================================
XrPosef
================================================================================
*/
XrPosef XrPosef_Identity() {
XrPosef r;
r.orientation.x = 0;
r.orientation.y = 0;
r.orientation.z = 0;
r.orientation.w = 1;
r.position.x = 0;
r.position.y = 0;
r.position.z = 0;
return r;
}
XrPosef XrPosef_Inverse(const XrPosef a) {
XrPosef b;
b.orientation = XrQuaternionf_Inverse(a.orientation);
b.position = XrQuaternionf_Rotate(b.orientation, XrVector3f_ScalarMultiply(a.position, -1.0f));
return b;
}
XrPosef XrPosef_Multiply(const XrPosef a, const XrPosef b) {
XrPosef c;
c.orientation = XrQuaternionf_Multiply(a.orientation, b.orientation);
c.position = XrPosef_Transform(a, b.position);
return c;
}
XrVector3f XrPosef_Transform(const XrPosef a, const XrVector3f v) {
XrVector3f r0 = XrQuaternionf_Rotate(a.orientation, v);
return XrVector3f_Add(r0, a.position);
}
/*
================================================================================
XrQuaternionf
================================================================================
*/
XrQuaternionf XrQuaternionf_CreateFromVectorAngle(const XrVector3f axis, const float angle) {
XrQuaternionf r;
if (XrVector3f_LengthSquared(axis) == 0.0f) {
r.x = 0;
r.y = 0;
r.z = 0;
r.w = 1;
return r;
}
XrVector3f unitAxis = XrVector3f_Normalized(axis);
float sinHalfAngle = sinf(angle * 0.5f);
r.w = cosf(angle * 0.5f);
r.x = unitAxis.x * sinHalfAngle;
r.y = unitAxis.y * sinHalfAngle;
r.z = unitAxis.z * sinHalfAngle;
return r;
}
XrQuaternionf XrQuaternionf_Inverse(const XrQuaternionf q) {
XrQuaternionf r;
r.x = -q.x;
r.y = -q.y;
r.z = -q.z;
r.w = q.w;
return r;
}
XrQuaternionf XrQuaternionf_Multiply(const XrQuaternionf a, const XrQuaternionf b) {
XrQuaternionf c;
c.x = a.w * b.x + a.x * b.w + a.y * b.z - a.z * b.y;
c.y = a.w * b.y - a.x * b.z + a.y * b.w + a.z * b.x;
c.z = a.w * b.z + a.x * b.y - a.y * b.x + a.z * b.w;
c.w = a.w * b.w - a.x * b.x - a.y * b.y - a.z * b.z;
return c;
}
XrVector3f XrQuaternionf_Rotate(const XrQuaternionf a, const XrVector3f v) {
XrVector3f r;
XrQuaternionf q = {v.x, v.y, v.z, 0.0f};
XrQuaternionf aq = XrQuaternionf_Multiply(a, q);
XrQuaternionf aInv = XrQuaternionf_Inverse(a);
XrQuaternionf aqaInv = XrQuaternionf_Multiply(aq, aInv);
r.x = aqaInv.x;
r.y = aqaInv.y;
r.z = aqaInv.z;
return r;
}
XrVector3f XrQuaternionf_ToEulerAngles(const XrQuaternionf q) {
ovrMatrix4f m = ovrMatrix4f_CreateFromQuaternion( &q );
return ovrMatrix4f_ToEulerAngles(&m);
}
/*
================================================================================
XrVector3f, XrVector4f
================================================================================
*/
float XrVector3f_Length(const XrVector3f v) {
return sqrtf(XrVector3f_LengthSquared(v));
}
float XrVector3f_LengthSquared(const XrVector3f v) {
return v.x * v.x + v.y * v.y + v.z * v.z;;
}
XrVector3f XrVector3f_Add(const XrVector3f u, const XrVector3f v) {
XrVector3f w;
w.x = u.x + v.x;
w.y = u.y + v.y;
w.z = u.z + v.z;
return w;
}
XrVector3f XrVector3f_GetAnglesFromVectors(const XrVector3f forward, const XrVector3f right, const XrVector3f up) {
float sr, sp, sy, cr, cp, cy;
sp = -forward.z;
float cp_x_cy = forward.x;
float cp_x_sy = forward.y;
float cp_x_sr = -right.z;
float cp_x_cr = up.z;
float yaw = atan2(cp_x_sy, cp_x_cy);
float roll = atan2(cp_x_sr, cp_x_cr);
cy = cos(yaw);
sy = sin(yaw);
cr = cos(roll);
sr = sin(roll);
if (fabs(cy) > EPSILON) {
cp = cp_x_cy / cy;
} else if (fabs(sy) > EPSILON) {
cp = cp_x_sy / sy;
} else if (fabs(sr) > EPSILON) {
cp = cp_x_sr / sr;
} else if (fabs(cr) > EPSILON) {
cp = cp_x_cr / cr;
} else {
cp = cos(asin(sp));
}
float pitch = atan2(sp, cp);
XrVector3f angles;
angles.x = ToDegrees(pitch);
angles.y = ToDegrees(yaw);
angles.z = ToDegrees(roll);
return angles;
}
XrVector3f XrVector3f_Normalized(const XrVector3f v) {
float rcpLen = 1.0f / XrVector3f_Length(v);
return XrVector3f_ScalarMultiply(v, rcpLen);
}
XrVector3f XrVector3f_ScalarMultiply(const XrVector3f v, float scale) {
XrVector3f u;
u.x = v.x * scale;
u.y = v.y * scale;
u.z = v.z * scale;
return u;
}
XrVector4f XrVector4f_MultiplyMatrix4f(const ovrMatrix4f* a, const XrVector4f* v) {
XrVector4f out;
out.x = a->M[0][0] * v->x + a->M[0][1] * v->y + a->M[0][2] * v->z + a->M[0][3] * v->w;
out.y = a->M[1][0] * v->x + a->M[1][1] * v->y + a->M[1][2] * v->z + a->M[1][3] * v->w;
out.z = a->M[2][0] * v->x + a->M[2][1] * v->y + a->M[2][2] * v->z + a->M[2][3] * v->w;
out.w = a->M[3][0] * v->x + a->M[3][1] * v->y + a->M[3][2] * v->z + a->M[3][3] * v->w;
return out;
}