Compare commits

12 Commits

Author SHA1 Message Date
af0421a557 clean up after merge 2023-11-16 19:46:41 +01:00
ef4251f664 clean up, add print method for springs, change Euler Function declaration, add demo, demo2 demo3 setup 2023-11-16 19:27:13 +01:00
MuZiQiAM
0647bb8735 TestCases, Midpoint push 2023-11-16 18:40:59 +01:00
82f103758d merge stuff demo 2 2023-11-08 15:19:29 +01:00
MuZiQiAM
03ebc33ec6 Merge branch 'master' of https://git.peroxy.dev/kookroach/game-physics 2023-11-08 15:14:20 +01:00
MuZiQiAM
3946a25f27 Demo 1 stuff 2023-11-08 15:14:17 +01:00
PfandBoss
741958d30b Mouse Input test stuff 2023-11-02 14:53:04 +01:00
047b913dfa Fix Repo + add basics 2023-10-31 00:37:29 +01:00
Felix Koehler
5348c6e002 Update build system for VS 2022 2023-10-30 07:47:16 +01:00
youxie
07934c01d5 Update quaternion.h
typo fix for quaternion multiplication
2022-11-09 16:19:52 +01:00
Brener
84e7c726c9 Including stdexcept in order to make retargeting to VS19 work 2021-10-22 09:38:59 +02:00
youxie
7170c0b8f0 Update readme.txt 2019-11-29 09:55:47 +01:00
26 changed files with 5069 additions and 56 deletions

47
.gitignore vendored Normal file
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# Prerequisites
*.d
# Compiled Object files
*.slo
*.lo
*.o
*.obj
# Precompiled Headers
*.gch
*.pch
# Compiled Dynamic libraries
*.so
*.dylib
*.dll
# Fortran module files
*.mod
*.smod
# Compiled Static libraries
*.lai
*.la
*.a
*.lib
# Executables
*.exe
*.out
*.app
.DS_STORE
Win32
*.vcxproj.user
.vs
SimulationsRunner/Debug
SimulationsRunner/Release
x64/
Win32/
Debug/
Release/

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@@ -0,0 +1,496 @@
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@@ -5748,8 +5748,13 @@ int ANT_CALL TwKeyTest(int _Key, int _Modifiers)
} }
// --------------------------------------------------------------------------- // ---------------------------------------------------------------------------
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struct StructCompare : public function<bool(TwType, TwType)>
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struct StructCompare : public binary_function<TwType, TwType, bool> struct StructCompare : public binary_function<TwType, TwType, bool>
#endif
{ {
bool operator()(const TwType& _Left, const TwType& _Right) const bool operator()(const TwType& _Left, const TwType& _Right) const
{ {

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8
Simulations/MassPoint.h Normal file
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#pragma once
#include "util/vectorbase.h"
struct MassPoint {
GamePhysics::Vec3 position;
GamePhysics::Vec3 velocity;
bool isFixed;
};

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#include "MassSpringSystemSimulator.h"
#include <stdio.h>
MassSpringSystemSimulator::MassSpringSystemSimulator()
{
m_iTestCase = 0;
m_fMass = 10;
m_fStiffness = 40;
m_iIntegrator = EULER;
}
const char* MassSpringSystemSimulator::getTestCasesStr()
{
return "Demo1,Demo2,Demo3,Demo4";
}
void MassSpringSystemSimulator::initUI(DrawingUtilitiesClass* DUC)
{
this->DUC = DUC;
switch (m_iTestCase)
{
case 0:
break;
case 1:
break;
case 2:
break;
default:
break;
}
}
void MassSpringSystemSimulator::reset()
{
m_mouse.x = m_mouse.y = 0;
m_trackmouse.x = m_trackmouse.y = 0;
m_oldtrackmouse.x = m_oldtrackmouse.y = 0;
springs.clear();
masspoints.clear();
}
void MassSpringSystemSimulator::drawFrame(ID3D11DeviceContext* pd3dImmediateContext)
{
for (size_t i = 0; i < springs.size(); i++) {
auto sp = springs.at(i);
if (!sp.isValid())
{
springs.erase(springs.begin() + i);
continue;
}
auto mp1 = sp.mp1.lock();
auto mp2 = sp.mp2.lock();
DUC->setUpLighting(Vec3(), 0.4 * Vec3(1, 1, 1), 100, 0.6 * Vec3(0.97, 0.86, 1));
DUC->drawSphere(mp1->position, Vec3(0.01));
DUC->drawSphere(mp2->position, Vec3(0.01));
DUC->beginLine();
DUC->drawLine(mp1->position, Vec3(1,0,0), mp2->position, Vec3(0,1,0));
DUC->endLine();
}
}
void MassSpringSystemSimulator::notifyCaseChanged(int testCase)
{
m_iTestCase = testCase;
system("cls");
reset();
switch (m_iTestCase)
{
case 0: {
cout << "Demo 1 !\n";
setMass(10);
setStiffness(40);
int first = addMassPoint(Vec3(0, 0, 0), Vec3(-1, 0, 0), true);
int second = addMassPoint(Vec3(0, 2, 0), Vec3(1, 0, 0), true);
addSpring(first, second, 1);
cout << "\t -- INITIAL --\n";
printSpring(springs.at(0));
cout << "--------------------------------------------------" << std::endl;
//calculate Euler for one step and print results
setIntegrator(EULER);
cout << "\n\n\t -- EULER RESULT --\n";
simulateTimestep(1);
printSpring(springs.at(0));
cout << "--------------------------------------------------" << std::endl;
reset();
first = addMassPoint(Vec3(0, 0, 0), Vec3(-1, 0, 0), true);
second = addMassPoint(Vec3(0, 2, 0), Vec3(1, 0, 0), true);
addSpring(first, second, 1);
//calculate Midpoint for one step and print results
setIntegrator(MIDPOINT);
cout << "\n\n\t -- MIDPOINT RESULT --\n";
simulateTimestep(1);
printSpring(springs.at(0));
break;
}
case 1: {
cout << "Demo 2 !\n";
reset();
int first = addMassPoint(Vec3(0, 0, 0), Vec3(-1, 0, 0), true);
int second = addMassPoint(Vec3(0, 2, 0), Vec3(1, 0, 0), true);
addSpring(first, second, 1.0);
cout << "\t -- INITIAL --\n";
printSpring(springs.at(0));
cout << "--------------------------------------------------" << std::endl;
//calculate Euler for a timestep of 0.005 and print results
setIntegrator(EULER);
cout << "\n\n\t -- EULER RESULT--\n";
simulateTimestep(0.005);
printSpring(springs.at(0));
break;
}
case 2: {
cout << "Demo 3 !\n";
reset();
int first = addMassPoint(Vec3(0, 0, 0), Vec3(-1, 0, 0), true);
int second = addMassPoint(Vec3(0, 2, 0), Vec3(1, 0, 0), true);
addSpring(first, second, 1.0);
cout << "\t -- INITIAL --\n";
printSpring(springs.at(0));
cout << "--------------------------------------------------" << std::endl;
//calculate Midpoint for a timestep of 0.005 and print results
setIntegrator(MIDPOINT);
cout << "\n\n\t -- MIDPOINT RESULT --\n";
simulateTimestep(0.005);
printSpring(springs.at(0));
break;
}
case 3: {
cout << "Demo 4 !\n";
break;
}
default:
break;
}
}
void MassSpringSystemSimulator::externalForcesCalculations(float timeElapsed)
{
Point2D mouseDiff;
mouseDiff.x = m_trackmouse.x - m_oldtrackmouse.x;
mouseDiff.y = m_trackmouse.y - m_oldtrackmouse.y;
if (mouseDiff.x != 0 || mouseDiff.y != 0)
{
Mat4 worldViewInv = Mat4(DUC->g_camera.GetWorldMatrix() * DUC->g_camera.GetViewMatrix());
worldViewInv = worldViewInv.inverse();
Vec3 inputView = Vec3((float)mouseDiff.x, (float)-mouseDiff.y, 0);
Vec3 inputWorld = worldViewInv.transformVectorNormal(inputView);
// find a proper scale!
float inputScale = 0.001f;
inputWorld = inputWorld * inputScale;
//m_vfMovableObjectPos = m_vfMovableObjectFinalPos + inputWorld;
}
else {
//m_vfMovableObjectFinalPos = m_vfMovableObjectPos;
}
}
void MassSpringSystemSimulator::simulateTimestep(float timeStep)
{
//update current setup for each frame
for (size_t i = 0; i < springs.size(); i++) {
auto sp = springs.at(i);
if (!sp.isValid())
{
springs.erase(springs.begin() + i);
continue;
}
if (m_iIntegrator == EULER) {
Euler(sp, timeStep);
}
else if (m_iIntegrator == MIDPOINT) {
Midpoint(sp, timeStep);
}
else if (m_iIntegrator == LEAPFROG) {
//TODO: Add Leapfrog
}
}
}
void MassSpringSystemSimulator::onClick(int x, int y)
{
m_trackmouse.x = x;
m_trackmouse.y = y;
}
void MassSpringSystemSimulator::onMouse(int x, int y)
{
m_oldtrackmouse.x = x;
m_oldtrackmouse.y = y;
m_trackmouse.x = x;
m_trackmouse.y = y;
}
void MassSpringSystemSimulator::setMass(float mass)
{
m_fMass = mass;
}
void MassSpringSystemSimulator::setStiffness(float stiffness)
{
m_fStiffness = stiffness;
}
void MassSpringSystemSimulator::setDampingFactor(float damping)
{
m_fDamping = damping;
}
int MassSpringSystemSimulator::addMassPoint(Vec3 position, Vec3 Velocity, bool isFixed)
{
MassPoint masspoint;
masspoint.position = position;
masspoint.velocity = Velocity;
masspoint.isFixed = isFixed;
masspoints.push_back(std::make_shared<MassPoint>(masspoint));
return masspoints.size() - 1;
}
void MassSpringSystemSimulator::addSpring(int masspoint1, int masspoint2, float initialLength)
{
auto mp1 = masspoints.at(masspoint1);
auto mp2 = masspoints.at(masspoint2);
Spring spring;
spring.mp1 = mp1;
spring.mp2 = mp2;
spring.initialLength = initialLength;
springs.push_back(spring);
}
int MassSpringSystemSimulator::getNumberOfMassPoints()
{
return masspoints.size();
}
int MassSpringSystemSimulator::getNumberOfSprings()
{
return springs.size();
}
Vec3 MassSpringSystemSimulator::getPositionOfMassPoint(int index)
{
auto mp = masspoints.at(index);
return mp->position;
}
Vec3 MassSpringSystemSimulator::getVelocityOfMassPoint(int index)
{
auto mp = masspoints.at(index);
return mp->velocity;
}
void MassSpringSystemSimulator::applyExternalForce(Vec3 force)
{
//eine Vorstellung: for all Masspoints, update force
}
int MassSpringSystemSimulator::LengthCalculator(Vec3 position1, Vec3 position2) {
Vec3 PosVector = position1 - position2;
//wurzel aus Vektor
int length = sqrt(pow(PosVector.x, 2) + pow(PosVector.y, 2) + pow(PosVector.z, 2));
return length;
}
Vec3 MassSpringSystemSimulator::calculatePositionTimestepEuler(Vec3 oldPosition, float timestep, Vec3 velocity)
{
return oldPosition + timestep * velocity;
}
Vec3 MassSpringSystemSimulator::calculateVelocityTimestepEuler(Vec3 oldVelocity, float timestep, Vec3 acceleration)
{
return oldVelocity + acceleration * timestep;
}
Vec3 MassSpringSystemSimulator::calculateAcceleration(Vec3 force, float mass)
{
return force / mass;
}
void MassSpringSystemSimulator::Midpoint(Spring& spring, float timestep) {
//here some implementation about Midpoint
auto massPoint1 = spring.mp1.lock();
auto massPoint2 = spring.mp2.lock();
//old position
auto mp = massPoint1->position;
auto mp2 = massPoint2->position;
//old Velocity
auto mOld_v = massPoint1->velocity;
auto m2Old_v = massPoint2->velocity;
Vec3 PosVector = mp - mp2;
//Abstand ausrechnen
int d = LengthCalculator(mp, mp2);
//normalize
Vec3 PosNorm1 = PosVector / d;
Vec3 PosNorm2 = -1 * PosNorm1;
Vec3 Force = -m_fStiffness * (d - springs.at(0).initialLength) * PosNorm1;
Vec3 Force2 = -1 * Force;
Vec3 oldAcc = calculateAcceleration(Force,m_fMass);
Vec3 oldAcc2 = calculateAcceleration(Force2, m_fMass);
//Midpoint calculator
//Pos of Midstep
Vec3 PosOfMidstep = mp + 0.5 * timestep * mOld_v;
Vec3 PosOfMidstep2 = mp2 + 0.5 * timestep * m2Old_v;
//Vel at Midstep
Vec3 VelAtMidstep = mOld_v + 0.5 * timestep * oldAcc;
Vec3 VelAtMidstep2 = m2Old_v + 0.5 * timestep * oldAcc2;
Vec3 NewPos = mp + timestep * VelAtMidstep;
Vec3 NewPos2 = mp2 + timestep * VelAtMidstep2;
Vec3 NewVel = mOld_v + timestep * oldAcc;
Vec3 NewVel2 = m2Old_v + timestep * oldAcc2;
//cout << NewPos;
//cout << NewVel;
massPoint1->position = NewPos;
massPoint1->velocity = NewVel;
massPoint2->position = NewPos2;
massPoint2->velocity = NewVel2;
}
void MassSpringSystemSimulator::Euler(Spring& spring, float timestep)
{
auto massPoint1 = spring.mp1.lock();
auto massPoint2 = spring.mp2.lock();
//take old position and send to calculatePositionTimestepEuler
auto PosVector = massPoint1->position - massPoint2->position;
auto lengthVector = sqrt(PosVector.x * PosVector.x + PosVector.y * PosVector.y + PosVector.z * PosVector.z);
auto normalized = PosVector / lengthVector;
// Actual Calculation
// Force of spring is -k * (l - L) * normalizedVector [for P2 we can take -F1)
auto force = -m_fStiffness * (lengthVector - spring.initialLength) * normalized;
auto foreP2 = -1 * force;
auto veloc = calculatePositionTimestepEuler(massPoint1->velocity, timestep, calculateAcceleration(force, 10.));
auto pos = calculatePositionTimestepEuler(massPoint1->position, timestep, veloc);
auto veloc2 = calculateVelocityTimestepEuler(massPoint2->velocity, timestep, calculateAcceleration(foreP2, 10.));
auto pos2 = calculatePositionTimestepEuler(massPoint2->position, timestep, veloc2);
// Update Positions and Velocity
massPoint1->position = pos;
massPoint1->velocity = veloc;
massPoint2->position = pos2;
massPoint2->velocity = veloc2;
}
void MassSpringSystemSimulator::printSpring(const Spring& spring)
{
auto mp1 = spring.mp1.lock();
auto mp2 = spring.mp2.lock();
printf("Masspoint 1:\nPosition: %s \nVelocity: %s\n\n", mp1->position.toString().c_str(), mp1->velocity.toString().c_str());
printf("Masspoint 2:\nPosition: %s \nVelocity: %s\n", mp2->position.toString().c_str(), mp2->velocity.toString().c_str());
}

View File

@@ -1,58 +1,74 @@
#ifndef MASSSPRINGSYSTEMSIMULATOR_h #ifndef MASSSPRINGSYSTEMSIMULATOR_h
#define MASSSPRINGSYSTEMSIMULATOR_h #define MASSSPRINGSYSTEMSIMULATOR_h
#include "Simulator.h" #include "Simulator.h"
#include "MassPoint.h"
// Do Not Change #include "Spring.h"
#define EULER 0
#define LEAPFROG 1 // Do Not Change
#define MIDPOINT 2 #define EULER 0
// Do Not Change #define LEAPFROG 1
#define MIDPOINT 2
// Do Not Change
class MassSpringSystemSimulator:public Simulator{
public:
// Construtors class MassSpringSystemSimulator:public Simulator{
MassSpringSystemSimulator(); public:
// Construtors
// UI Functions MassSpringSystemSimulator();
const char * getTestCasesStr();
void initUI(DrawingUtilitiesClass * DUC); // UI Functions
void reset(); const char * getTestCasesStr();
void drawFrame(ID3D11DeviceContext* pd3dImmediateContext); void initUI(DrawingUtilitiesClass * DUC);
void notifyCaseChanged(int testCase); void reset();
void externalForcesCalculations(float timeElapsed); void drawFrame(ID3D11DeviceContext* pd3dImmediateContext);
void simulateTimestep(float timeStep); void notifyCaseChanged(int testCase);
void onClick(int x, int y); void externalForcesCalculations(float timeElapsed);
void onMouse(int x, int y); void simulateTimestep(float timeStep);
void onClick(int x, int y);
// Specific Functions void onMouse(int x, int y);
void setMass(float mass);
void setStiffness(float stiffness); // Specific Functions
void setDampingFactor(float damping); void setMass(float mass);
int addMassPoint(Vec3 position, Vec3 Velocity, bool isFixed); void setStiffness(float stiffness);
void addSpring(int masspoint1, int masspoint2, float initialLength); void setDampingFactor(float damping);
int getNumberOfMassPoints(); int addMassPoint(Vec3 position, Vec3 Velocity, bool isFixed);
int getNumberOfSprings(); void addSpring(int masspoint1, int masspoint2, float initialLength);
Vec3 getPositionOfMassPoint(int index); int getNumberOfMassPoints();
Vec3 getVelocityOfMassPoint(int index); int getNumberOfSprings();
Vec3 getPositionOfMassPoint(int index);
Vec3 getVelocityOfMassPoint(int index);
void applyExternalForce(Vec3 force); void applyExternalForce(Vec3 force);
void Midpoint(Spring& spring, float timestep);
int LengthCalculator(Vec3 position1, Vec3 position2);
Vec3 calculatePositionTimestepEuler(Vec3 oldPosition, float timestep, Vec3 veloctiy);
Vec3 calculateVelocityTimestepEuler(Vec3 oldVelocity, float timestep, Vec3 acceleration);
Vec3 calculateAcceleration(Vec3 acceleration, float mass);
void Euler(Spring& spring, float timestep);
void printSpring(const Spring& spring);
// Do Not Change // Do Not Change
void setIntegrator(int integrator) { void setIntegrator(int integrator) {
m_iIntegrator = integrator; m_iIntegrator = integrator;
} }
private: private:
// Data Attributes // Data Attributes
float m_fMass; float m_fMass;
float m_fStiffness; float m_fStiffness;
float m_fDamping; float m_fDamping;
int m_iIntegrator; int m_iIntegrator;
// UI Attributes // UI Attributes
Vec3 m_externalForce; Vec3 m_externalForce;
Point2D m_mouse; Point2D m_mouse;
Point2D m_trackmouse; Point2D m_trackmouse;
Point2D m_oldtrackmouse; Point2D m_oldtrackmouse;
};
//Mass points and springs
std::vector<std::shared_ptr<MassPoint>> masspoints;
std::vector<Spring> springs;
};
#endif #endif

0
Simulations/Spring.cpp Normal file
View File

11
Simulations/Spring.h Normal file
View File

@@ -0,0 +1,11 @@
#pragma once
struct Spring
{
std::weak_ptr<MassPoint> mp1;
std::weak_ptr<MassPoint> mp2;
float initialLength;
bool isValid() { return !mp1.expired() && !mp2.expired(); }
};

View File

@@ -20,8 +20,8 @@ using namespace GamePhysics;
//#define ADAPTIVESTEP //#define ADAPTIVESTEP
#define TEMPLATE_DEMO //#define TEMPLATE_DEMO
//#define MASS_SPRING_SYSTEM #define MASS_SPRING_SYSTEM
//#define RIGID_BODY_SYSTEM //#define RIGID_BODY_SYSTEM
//#define SPH_SYSTEM //#define SPH_SYSTEM
@@ -53,9 +53,14 @@ bool firstTime = true;
FFmpeg* g_pFFmpegVideoRecorder = nullptr; FFmpeg* g_pFFmpegVideoRecorder = nullptr;
// Input Stuff
float lastX;
float lastY;
void initTweakBar(){ void initTweakBar(){
g_pDUC->g_pTweakBar = TwNewBar("TweakBar"); g_pDUC->g_pTweakBar = TwNewBar("TweakBar");
TwDefine(" TweakBar color='0 128 128' alpha=128 "); TwDefine(" TweakBar color='128 128 128' alpha=128 ");
TwType TW_TYPE_TESTCASE = TwDefineEnumFromString("Test Scene", g_pSimulator->getTestCasesStr()); TwType TW_TYPE_TESTCASE = TwDefineEnumFromString("Test Scene", g_pSimulator->getTestCasesStr());
TwAddVarRW(g_pDUC->g_pTweakBar, "Test Scene", TW_TYPE_TESTCASE, &g_iTestCase, ""); TwAddVarRW(g_pDUC->g_pTweakBar, "Test Scene", TW_TYPE_TESTCASE, &g_iTestCase, "");
// HINT: For buttons you can directly pass the callback function as a lambda expression. // HINT: For buttons you can directly pass the callback function as a lambda expression.
@@ -202,10 +207,23 @@ void CALLBACK OnMouse( bool bLeftButtonDown, bool bRightButtonDown, bool bMiddle
if (bLeftButtonDown) if (bLeftButtonDown)
{ {
g_pSimulator->onClick(xPos,yPos); g_pSimulator->onClick(xPos,yPos);
int x = xPos;
int y = yPos;
} }
else else
{ {
g_pSimulator->onMouse(xPos, yPos); g_pSimulator->onMouse(xPos, yPos);
float deltaX = lastX - xPos;
float deltaY = lastY - yPos;
lastX = xPos;
lastY = yPos;
/*printf("X Delta: %f \n", deltaX);
printf("Y Delta: %f \n", deltaY);*/
} }
} }

View File

@@ -83,7 +83,7 @@ public:
inline const Quaternion operator*=(const Quaternion &q) inline const Quaternion operator*=(const Quaternion &q)
{ {
vector3Dim<Scalar> v1(x,y,z), v2(q.x,q.y,q.z); vector3Dim<Scalar> v1(x,y,z), v2(q.x,q.y,q.z);
vector3Dim<Scalar> nv = v1*q.w + v2*w + cross(v2,v1); vector3Dim<Scalar> nv = v1*q.w + v2*w + cross(v1,v2);
Scalar nw = w*q.w - (v1.x*v2.x+v1.y*v2.y+v1.z*v2.z); Scalar nw = w*q.w - (v1.x*v2.x+v1.y*v2.y+v1.z*v2.z);
x = nv.x; x = nv.x;
y = nv.y; y = nv.y;
@@ -106,7 +106,7 @@ public:
inline const Quaternion operator*(const Quaternion &q) const inline const Quaternion operator*(const Quaternion &q) const
{ {
vector3Dim<Scalar> v1(x,y,z), v2(q.x,q.y,q.z); vector3Dim<Scalar> v1(x,y,z), v2(q.x,q.y,q.z);
vector3Dim<Scalar> nv = v1*q.w + v2*w + cross(v2,v1); vector3Dim<Scalar> nv = v1*q.w + v2*w + cross(v1,v2);
Scalar nw = w*q.w - (v1.x*v2.x+v1.y*v2.y+v1.z*v2.z); Scalar nw = w*q.w - (v1.x*v2.x+v1.y*v2.y+v1.z*v2.z);
return Quaternion(nv.x,nv.y,nv.z,nw); return Quaternion(nv.x,nv.y,nv.z,nw);

View File

@@ -0,0 +1,239 @@
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------------------------------------------------------------------------------- -------------------------------------------------------------------------------
--- Visual Studio 2013/15/17 Template Project for C++/DirectX11 Application --- --- Visual Studio 2013/15/17/22 Template Project for C++/DirectX11 Application
--- Marc Treib, Florian Ferstl, Sept 2013 ------------------------------------- --- Marc Treib, Florian Ferstl, Sept 2013 -------------------------------------
--- Updated: Florian Ferstl, Sept 2014 ---------------------------------------- --- Updated: Florian Ferstl, Sept 2014 ----------------------------------------
--- Updated: Mina Saad Aziz, May 2016 ----------------------------------------- --- Updated: Mina Saad Aziz, May 2016 -----------------------------------------
--- Updated: Mengyu Chu, Nov 2017 ------------------------------------------ --- Updated: Mengyu Chu, Nov 2017 ------------------------------------------
--- Updated: You Xie, Nov 2019 ---------------------------------------------
--- Updated: Rene Winchenbach, Felix Koehler, Oct 2023 ---------------------
------------------------------------------------------------------------------- -------------------------------------------------------------------------------
!Important:
We recommend using the `Template_2022.sln` solution file together with Visual
Studio 2022 Community Edition.
This solution contains the following components: This solution contains the following components:
- AntTweakBar 1.16 - AntTweakBar 1.16
@@ -45,4 +52,4 @@ Further Note:
DXUT are both based on the new DirectXMath API for linear algebra that comes DXUT are both based on the new DirectXMath API for linear algebra that comes
with the Windows 8.* SDKs (replacing the old D3DXMath). You can use it for with the Windows 8.* SDKs (replacing the old D3DXMath). You can use it for
all of your linear algebra tasks. all of your linear algebra tasks.
Documentation: https://msdn.microsoft.com/en-us/library/windows/desktop/hh437833(v=vs.85).aspx Documentation: https://msdn.microsoft.com/en-us/library/windows/desktop/hh437833(v=vs.85).aspx