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Implemented a custom physics engine #316

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direnbharwani merged 95 commits from SHPhysics into main 2023-01-23 15:55:45 +08:00
Conversation 0 Commits 95 Files Changed 144 +128 -41
7 changed files with 128 additions and 41 deletions
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4
Assets/Scenes/PhysicsSandbox.shade
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@ -280,7 +280,7 @@
NumberOfChildren: 0
Components:
Transform Component:
Translate: {x: 0.524352431, y: 11.5, z: 0.0463808179}
Translate: {x: 0.524352431, y: 13.5, z: 0.0463808179}
Rotate: {x: -0, y: 0.785398066, z: 0.785398185}
Scale: {x: 0.999999821, y: 0.999999821, z: 0.999999881}
IsActive: true
@ -291,7 +291,7 @@
Drag: 0.00999999978
Angular Drag: 0.00999999978
Use Gravity: true
Gravity Scale: 1
Gravity Scale: 0.5
Interpolate: true
Sleeping Enabled: true
Freeze Position X: false

3
SHADE_Engine/src/Physics/Collision/Narrowphase/SHCollision.h
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@ -108,6 +108,7 @@ namespace SHADE
static bool isMinkowskiFace (const SHVec3& a, const SHVec3& b, const SHVec3& c, const SHVec3& d) noexcept;
static float distanceBetweenEdges (const SHConvexPolyhedron& A, const SHConvexPolyhedron& B, int32_t edgeA, int32_t edgeB) noexcept;
static SHVec3 findClosestPointBetweenEdges (const SHConvexPolyhedron& A, const SHConvexPolyhedron& B, int32_t edgeA, int32_t edgeB) noexcept;
static int32_t findIncidentFace (const SHConvexPolyhedron& poly, const SHVec3& normal) noexcept;
/*
* TODO:
@ -115,7 +116,7 @@ namespace SHADE
*
*
*
* static int32_t findIncidentFace (SHConvexPolyhedron& poly, const SHVec3& normal) noexcept;
*
* static uint32_t clip [sutherland-hodgemann clipping]
*
* ! References

107
SHADE_Engine/src/Physics/Collision/Narrowphase/SHConvexVsConvex.cpp
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@ -17,6 +17,7 @@
#include "Math/SHMathHelpers.h"
#include "Math/Geometry/SHPlane.h"
#include "Physics/Collision/Shapes/SHConvexPolyhedron.h"
#include "Physics/SHPhysicsConstants.h"
#include "Tools/Utilities/SHUtilities.h"
namespace SHADE
@ -47,24 +48,7 @@ namespace SHADE
bool SHCollision::ConvexVsConvex(SHManifold& manifold, const SHCollisionShape& A, const SHCollisionShape& B) noexcept
{
/*
* TODO:
*
* 1. Query face directions of a to b. Exit early if separation found.
* 2. Query face directions of b to a. Exit early if separation found.
* 3. Query edge directions of a & b. Exit early if separation found.
*
* (*)!! Apply weight to improve frame coherence of normal directions. DONT FORGET FLIP FLOP!
* 4. From above, save the axis of minimum penetration (reference face)
* 5. Find the most anti-parallel face on other shape (incident face)
* 6. Clip incident face against side planes of reference face. (Sutherland-Hodgeman Clipping).
* Keep all vertices below reference face.
* 7. Reduce manifold to 4 contact points. We only need 4 contact points for a stable manifold.
*
* Remember to save IDs in queries.
* During generation of incident face, store IDs of face.
*
*/
static constexpr float TOLERANCE = 0.1f + SHPHYSICS_LINEAR_SLOP;
const SHConvexPolyhedron& POLY_A = dynamic_cast<const SHConvexPolyhedron&>(A);
const SHConvexPolyhedron& POLY_B = dynamic_cast<const SHConvexPolyhedron&>(B);
@ -81,14 +65,33 @@ namespace SHADE
if (EDGE_QUERY.bestDistance > 0.0f)
return false;
const FaceQuery& BEST_FACE_QUERY = FACE_QUERY_A.bestDistance > FACE_QUERY_B.bestDistance ? FACE_QUERY_A : FACE_QUERY_B;
// Apply weight to improve frame coherence of normal directions.
// We want a normal in the direction from A -> B, so we flip the normal if needed.
bool flipNormal = false;
const SHConvexPolyhedron* referencePoly = nullptr;
const SHConvexPolyhedron* incidentPoly = nullptr;
FaceQuery minFaceQuery;
if (FACE_QUERY_A.bestDistance + TOLERANCE > FACE_QUERY_B.bestDistance)
{
minFaceQuery = FACE_QUERY_A;
referencePoly = &POLY_A;
incidentPoly = &POLY_B;
}
else
{
minFaceQuery = FACE_QUERY_B;
referencePoly = &POLY_B;
incidentPoly = &POLY_A;
flipNormal = true;
}
uint32_t numContacts = 0;
// If an edge pair contains the closest distance,vwe ignore any face queries and find the closest points on
// each edge and use that as the contact point.
// Artificially increase the depth of this collision by a small tolerance to tend towards picking a face query in the next frame.
if (EDGE_QUERY.bestDistance > BEST_FACE_QUERY.bestDistance)
if (EDGE_QUERY.bestDistance > minFaceQuery.bestDistance + TOLERANCE)
{
const SHHalfEdgeStructure::HalfEdge& HALF_EDGE_A = POLY_A.GetHalfEdge(EDGE_QUERY.halfEdgeA);
const SHHalfEdgeStructure::HalfEdge& HALF_EDGE_B = POLY_B.GetHalfEdge(EDGE_QUERY.halfEdgeB);
@ -122,7 +125,24 @@ namespace SHADE
return true;
}
// Use a bias to favour a normal in the direction of A -> B
const SHVec3 REFERENCE_NORMAL = referencePoly->GetNormal(minFaceQuery.closestFace);
const int32_t INCIDENT_FACE_IDX = findIncidentFace(*incidentPoly, REFERENCE_NORMAL);
/*
* TODO:
*
* !!
* 4. From above, save the axis of minimum penetration (reference face)
* 5. Find the most anti-parallel face on other shape (incident face)
* 6. Clip incident face against side planes of reference face. (Sutherland-Hodgeman Clipping).
* Keep all vertices below reference face.
* 7. Reduce manifold to 4 contact points. We only need 4 contact points for a stable manifold.
*
* Remember to save IDs in queries.
* During generation of incident face, store IDs of face.
*
*/
@ -289,25 +309,48 @@ namespace SHADE
const SHVec3 C = TAIL_B - TAIL_A;
const float VB_DOT_VA = SHVec3::Dot(VB, VA);
const float VB_DOT_VB = SHVec3::Dot(VB, VB);
const float AV_DOT_VA = SHVec3::Dot(-VA, VA);
const float AV_DOT_VB = SHVec3::Dot(-VA, VB);
const float C_DOT_VA = SHVec3::Dot(C, VA);
const float C_DOT_VB = SHVec3::Dot(C, VB);
const float VB_DOT_VA = SHVec3::Dot(VB, VA); // a1
const float VB_DOT_VB = SHVec3::Dot(VB, VB); // a2
const float AV_DOT_VA = SHVec3::Dot(-VA, VA); // b1
const float AV_DOT_VB = SHVec3::Dot(-VA, VB); // b2
const float C_DOT_VA = SHVec3::Dot(C, VA); // c1
const float C_DOT_VB = SHVec3::Dot(C, VB); // c2
/*
* R = -c2 / ( b2 - (a2 * (c1 + b1)) / a1 )
* S = (b1 / a1) * (c2 / ( b2 - (a2 * b1) / a1 )) - (c1 / a1)
*
* We only need to solve for R
* R = (c1a2 / a1 - c2) / ( b2 - a2b1/a1 )
*/
const float R = -C_DOT_VB / (AV_DOT_VB - (VB_DOT_VB * (C_DOT_VA + AV_DOT_VA)) / VB_DOT_VA);
const float A2_OVER_A1 = VB_DOT_VB / VB_DOT_VA;
const float NUMERATOR = C_DOT_VA * A2_OVER_A1 - C_DOT_VB;
const float DENOMINATOR = AV_DOT_VB - AV_DOT_VA * A2_OVER_A1;
const float R = NUMERATOR / DENOMINATOR;
// Just take a point from A since it's A -> B
return TAIL_A + R * VA;
}
int32_t SHCollision::findIncidentFace(const SHConvexPolyhedron& poly, const SHVec3& normal) noexcept
{
// Get the most anti-parallel face to the normal
int32_t bestFace = 0;
float bestProjection = std::numeric_limits<float>::max();
const int32_t NUM_FACES = poly.GetFaceCount();
for (const int32_t i : std::views::iota(0, NUM_FACES))
{
const SHVec3 INC_NORMAL = poly.GetNormal(i);
const float PROJECTION = SHVec3::Dot(INC_NORMAL, normal);
if (PROJECTION < bestProjection)
{
bestProjection = PROJECTION;
bestFace = i;
}
}
return bestFace;
}
} // namespace SHADE

1
SHADE_Engine/src/Physics/Collision/Narrowphase/SHSphereVsConvex.cpp
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@ -19,6 +19,7 @@
#include "Math/SHMathHelpers.h"
#include "Physics/Collision/Shapes/SHSphere.h"
#include "Physics/Collision/Shapes/SHConvexPolyhedron.h"
#include "Physics/SHPhysicsConstants.h"
namespace SHADE
{

5
SHADE_Engine/src/Physics/Dynamics/SHContactSolver.cpp
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@ -15,6 +15,7 @@
// Project Headers
#include "Math/SHMathHelpers.h"
#include "Physics/SHPhysicsConstants.h"
namespace SHADE
{
@ -190,8 +191,8 @@ namespace SHADE
const SHVec3 RV_B = vB + SHVec3::Cross(wB, contact.rB);
const float RV_N = SHVec3::Dot(RV_B - RV_A, constraint.normal);
const float ERROR_BIAS = BAUMGARTE_FACTOR * INV_DT * std::min(0.0f, -contact.penetration + PENETRATION_SLOP);
const float RESTITUTION_BIAS = -constraint.restitution * RV_N;
const float ERROR_BIAS = SHPHYSICS_BAUMGARTE * INV_DT * std::min(0.0f, -contact.penetration + SHPHYSICS_LINEAR_SLOP);
const float RESTITUTION_BIAS = std::fabs(RV_N) > SHPHYSICS_RESTITUTION_THRESHOLD ? -constraint.restitution * RV_N : 0.0f;
contact.bias = ERROR_BIAS + RESTITUTION_BIAS;

3
SHADE_Engine/src/Physics/Dynamics/SHContactSolver.h
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@ -78,9 +78,6 @@ namespace SHADE
/* Data Members */
/*---------------------------------------------------------------------------------*/
static constexpr float BAUMGARTE_FACTOR = 0.2f;
static constexpr float PENETRATION_SLOP = 0.05f;
VelocityStates velocityStates;
ContactConstraints contactConstraints;

44
SHADE_Engine/src/Physics/SHPhysicsConstants.h Normal file
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@ -0,0 +1,44 @@
/****************************************************************************************
* \file SHPhysicsConstants.h
* \author Diren D Bharwani, diren.dbharwani, 390002520
* \brief Definitions for constants used in physics simulations
*
* \copyright Copyright (C) 2022 DigiPen Institute of Technology. Reproduction or
* disclosure of this file or its contents without the prior written consent
* of DigiPen Institute of Technology is prohibited.
****************************************************************************************/
#pragma once
// Project Includes
#include "Math/SHMathHelpers.h"
namespace SHADE
{
/**
* @brief
* The number of simulations length for every real world unit meter. <br/>
* Modify this to change the global scale of the simulation.
*/
static constexpr float SHPHYSICS_LENGTHS_PER_UNIT_METER = 1.0f;
/**
* @brief
* Linear Collision & Constraint tolerance.
*/
static constexpr float SHPHYSICS_LINEAR_SLOP = 0.005f * SHPHYSICS_LENGTHS_PER_UNIT_METER;
/**
* @brief
* Velocity threshold for restitution to be applied.
*/
static constexpr float SHPHYSICS_RESTITUTION_THRESHOLD = 1.0f;
/**
* @brief
* Scaling factor to control how fast overlaps are resolved.<br/>
* 1 is ideal for instant correction, but values close to 1 can lead to overshoot.
*/
static constexpr float SHPHYSICS_BAUMGARTE = 0.2f;
}