/********************************************************************************************** * * Physac v1.1 - 2D Physics library for videogames * * DESCRIPTION: * * Physac is a small 2D physics engine written in pure C. The engine uses a fixed time-step thread loop * to simluate physics. A physics step contains the following phases: get collision information, * apply dynamics, collision solving and position correction. It uses a very simple struct for physic * bodies with a position vector to be used in any 3D rendering API. * * CONFIGURATION: * * #define PHYSAC_IMPLEMENTATION * Generates the implementation of the library into the included file. * If not defined, the library is in header only mode and can be included in other headers * or source files without problems. But only ONE file should hold the implementation. * * #define PHYSAC_DEBUG * Show debug traces log messages about physic bodies creation/destruction, physic system errors, * some calculations results and NULL reference exceptions. * * #define PHYSAC_AVOID_TIMMING_SYSTEM * Disables internal timming system, used by UpdatePhysics() to launch timmed physic steps, * it allows just running UpdatePhysics() automatically on a separate thread at a desired time step. * In case physics steps update needs to be controlled by user with a custom timming mechanism, * just define this flag and the internal timming mechanism will be avoided, in that case, * timming libraries are neither required by the module. * * #define PHYSAC_MALLOC() * #define PHYSAC_CALLOC() * #define PHYSAC_FREE() * You can define your own malloc/free implementation replacing stdlib.h malloc()/free() functions. * Otherwise it will include stdlib.h and use the C standard library malloc()/free() function. * * COMPILATION: * * Use the following code to compile with GCC: * gcc -o $(NAME_PART).exe $(FILE_NAME) -s -static -lraylib -lopengl32 -lgdi32 -lwinmm -std=c99 * * VERSIONS HISTORY: * 1.1 (20-Jan-2021) @raysan5: Library general revision * Removed threading system (up to the user) * Support MSVC C++ compilation using CLITERAL() * Review DEBUG mechanism for TRACELOG() and all TRACELOG() messages * Review internal variables/functions naming for consistency * Allow option to avoid internal timming system, to allow app manage the steps * 1.0 (12-Jun-2017) First release of the library * * * LICENSE: zlib/libpng * * Copyright (c) 2016-2021 Victor Fisac (@victorfisac) and Ramon Santamaria (@raysan5) * * This software is provided "as-is", without any express or implied warranty. In no event * will the authors be held liable for any damages arising from the use of this software. * * Permission is granted to anyone to use this software for any purpose, including commercial * applications, and to alter it and redistribute it freely, subject to the following restrictions: * * 1. The origin of this software must not be misrepresented; you must not claim that you * wrote the original software. If you use this software in a product, an acknowledgment * in the product documentation would be appreciated but is not required. * * 2. Altered source versions must be plainly marked as such, and must not be misrepresented * as being the original software. * * 3. This notice may not be removed or altered from any source distribution. * **********************************************************************************************/ #if !defined(PHYSAC_H) #define PHYSAC_H #ifndef PHYSACDEF #define PHYSACDEF // We are building or using physac as a static library #endif // Allow custom memory allocators #ifndef PHYSAC_MALLOC #define PHYSAC_MALLOC(size) malloc(size) #endif #ifndef PHYSAC_CALLOC #define PHYSAC_CALLOC(size, n) calloc(size, n) #endif #ifndef PHYSAC_FREE #define PHYSAC_FREE(ptr) free(ptr) #endif //---------------------------------------------------------------------------------- // Defines and Macros //---------------------------------------------------------------------------------- #define PHYSAC_MAX_BODIES 64 // Maximum number of physic bodies supported #define PHYSAC_MAX_MANIFOLDS 4096 // Maximum number of physic bodies interactions (64x64) #define PHYSAC_MAX_VERTICES 24 // Maximum number of vertex for polygons shapes #define PHYSAC_DEFAULT_CIRCLE_VERTICES 24 // Default number of vertices for circle shapes #define PHYSAC_COLLISION_ITERATIONS 100 #define PHYSAC_PENETRATION_ALLOWANCE 0.05f #define PHYSAC_PENETRATION_CORRECTION 0.4f #define PHYSAC_PI 3.14159265358979323846f #define PHYSAC_DEG2RAD (PHYSAC_PI/180.0f) //---------------------------------------------------------------------------------- // Data Types Structure Definition //---------------------------------------------------------------------------------- #if defined(__STDC__) && __STDC_VERSION__ >= 199901L #include #endif typedef enum PhysicsShapeType { PHYSICS_CIRCLE = 0, PHYSICS_POLYGON } PhysicsShapeType; // Previously defined to be used in PhysicsShape struct as circular dependencies typedef struct PhysicsBodyData *PhysicsBody; #if !defined(RL_VECTOR2_TYPE) // Vector2 type typedef struct Vector2 { float x; float y; } Vector2; #endif // Matrix2x2 type (used for polygon shape rotation matrix) typedef struct Matrix2x2 { float m00; float m01; float m10; float m11; } Matrix2x2; typedef struct PhysicsVertexData { unsigned int vertexCount; // Vertex count (positions and normals) Vector2 positions[PHYSAC_MAX_VERTICES]; // Vertex positions vectors Vector2 normals[PHYSAC_MAX_VERTICES]; // Vertex normals vectors } PhysicsVertexData; typedef struct PhysicsShape { PhysicsShapeType type; // Shape type (circle or polygon) PhysicsBody body; // Shape physics body data pointer PhysicsVertexData vertexData; // Shape vertices data (used for polygon shapes) float radius; // Shape radius (used for circle shapes) Matrix2x2 transform; // Vertices transform matrix 2x2 } PhysicsShape; typedef struct PhysicsBodyData { unsigned int id; // Unique identifier bool enabled; // Enabled dynamics state (collisions are calculated anyway) Vector2 position; // Physics body shape pivot Vector2 velocity; // Current linear velocity applied to position Vector2 force; // Current linear force (reset to 0 every step) float angularVelocity; // Current angular velocity applied to orient float torque; // Current angular force (reset to 0 every step) float orient; // Rotation in radians float inertia; // Moment of inertia float inverseInertia; // Inverse value of inertia float mass; // Physics body mass float inverseMass; // Inverse value of mass float staticFriction; // Friction when the body has not movement (0 to 1) float dynamicFriction; // Friction when the body has movement (0 to 1) float restitution; // Restitution coefficient of the body (0 to 1) bool useGravity; // Apply gravity force to dynamics bool isGrounded; // Physics grounded on other body state bool freezeOrient; // Physics rotation constraint PhysicsShape shape; // Physics body shape information (type, radius, vertices, transform) } PhysicsBodyData; typedef struct PhysicsManifoldData { unsigned int id; // Unique identifier PhysicsBody bodyA; // Manifold first physics body reference PhysicsBody bodyB; // Manifold second physics body reference float penetration; // Depth of penetration from collision Vector2 normal; // Normal direction vector from 'a' to 'b' Vector2 contacts[2]; // Points of contact during collision unsigned int contactsCount; // Current collision number of contacts float restitution; // Mixed restitution during collision float dynamicFriction; // Mixed dynamic friction during collision float staticFriction; // Mixed static friction during collision } PhysicsManifoldData, *PhysicsManifold; //---------------------------------------------------------------------------------- // Module Functions Declaration //---------------------------------------------------------------------------------- #if defined(__cplusplus) extern "C" { // Prevents name mangling of functions #endif // Physics system management PHYSACDEF void InitPhysics(void); // Initializes physics system PHYSACDEF void UpdatePhysics(void); // Update physics system PHYSACDEF void ResetPhysics(void); // Reset physics system (global variables) PHYSACDEF void ClosePhysics(void); // Close physics system and unload used memory PHYSACDEF void SetPhysicsTimeStep(double delta); // Sets physics fixed time step in milliseconds. 1.666666 by default PHYSACDEF void SetPhysicsGravity(float x, float y); // Sets physics global gravity force // Physic body creation/destroy PHYSACDEF PhysicsBody CreatePhysicsBodyCircle(Vector2 pos, float radius, float density); // Creates a new circle physics body with generic parameters PHYSACDEF PhysicsBody CreatePhysicsBodyRectangle(Vector2 pos, float width, float height, float density); // Creates a new rectangle physics body with generic parameters PHYSACDEF PhysicsBody CreatePhysicsBodyPolygon(Vector2 pos, float radius, int sides, float density); // Creates a new polygon physics body with generic parameters PHYSACDEF void DestroyPhysicsBody(PhysicsBody body); // Destroy a physics body // Physic body forces PHYSACDEF void PhysicsAddForce(PhysicsBody body, Vector2 force); // Adds a force to a physics body PHYSACDEF void PhysicsAddTorque(PhysicsBody body, float amount); // Adds an angular force to a physics body PHYSACDEF void PhysicsShatter(PhysicsBody body, Vector2 position, float force); // Shatters a polygon shape physics body to little physics bodies with explosion force PHYSACDEF void SetPhysicsBodyRotation(PhysicsBody body, float radians); // Sets physics body shape transform based on radians parameter // Query physics info PHYSACDEF PhysicsBody GetPhysicsBody(int index); // Returns a physics body of the bodies pool at a specific index PHYSACDEF int GetPhysicsBodiesCount(void); // Returns the current amount of created physics bodies PHYSACDEF int GetPhysicsShapeType(int index); // Returns the physics body shape type (PHYSICS_CIRCLE or PHYSICS_POLYGON) PHYSACDEF int GetPhysicsShapeVerticesCount(int index); // Returns the amount of vertices of a physics body shape PHYSACDEF Vector2 GetPhysicsShapeVertex(PhysicsBody body, int vertex); // Returns transformed position of a body shape (body position + vertex transformed position) #if defined(__cplusplus) } #endif #endif // PHYSAC_H /*********************************************************************************** * * PHYSAC IMPLEMENTATION * ************************************************************************************/ #if defined(PHYSAC_IMPLEMENTATION) // Support TRACELOG macros #if defined(PHYSAC_DEBUG) #include // Required for: printf() #define TRACELOG(...) printf(__VA_ARGS__) #else #define TRACELOG(...) (void)0; #endif #include // Required for: malloc(), calloc(), free() #include // Required for: cosf(), sinf(), fabs(), sqrtf() #if !defined(PHYSAC_AVOID_TIMMING_SYSTEM) // Time management functionality #include // Required for: time(), clock_gettime() #if defined(_WIN32) #if defined(__cplusplus) extern "C" { // Prevents name mangling of functions #endif // Functions required to query time on Windows int __stdcall QueryPerformanceCounter(unsigned long long int *lpPerformanceCount); int __stdcall QueryPerformanceFrequency(unsigned long long int *lpFrequency); #if defined(__cplusplus) } #endif #endif #if defined(__linux__) || defined(__FreeBSD__) #if _POSIX_C_SOURCE < 199309L #undef _POSIX_C_SOURCE #define _POSIX_C_SOURCE 199309L // Required for CLOCK_MONOTONIC if compiled with c99 without gnu ext. #endif #include // Required for: timespec #endif #if defined(__APPLE__) // macOS also defines __MACH__ #include // Required for: mach_absolute_time() #endif #endif // NOTE: MSVC C++ compiler does not support compound literals (C99 feature) // Plain structures in C++ (without constructors) can be initialized from { } initializers. #if defined(__cplusplus) #define CLITERAL(type) type #else #define CLITERAL(type) (type) #endif //---------------------------------------------------------------------------------- // Defines and Macros //---------------------------------------------------------------------------------- #define PHYSAC_MIN(a,b) (((a)<(b))?(a):(b)) #define PHYSAC_MAX(a,b) (((a)>(b))?(a):(b)) #define PHYSAC_FLT_MAX 3.402823466e+38f #define PHYSAC_EPSILON 0.000001f #define PHYSAC_K 1.0f/3.0f #define PHYSAC_VECTOR_ZERO CLITERAL(Vector2){ 0.0f, 0.0f } //---------------------------------------------------------------------------------- // Global Variables Definition //---------------------------------------------------------------------------------- static double deltaTime = 1.0/60.0/10.0 * 1000; // Delta time in milliseconds used for physics steps #if !defined(PHYSAC_AVOID_TIMMING_SYSTEM) // Time measure variables static double baseClockTicks = 0.0; // Offset clock ticks for MONOTONIC clock static unsigned long long int frequency = 0; // Hi-res clock frequency static double startTime = 0.0; // Start time in milliseconds static double currentTime = 0.0; // Current time in milliseconds #endif // Physics system configuration static PhysicsBody bodies[PHYSAC_MAX_BODIES]; // Physics bodies pointers array static unsigned int physicsBodiesCount = 0; // Physics world current bodies counter static PhysicsManifold contacts[PHYSAC_MAX_MANIFOLDS]; // Physics bodies pointers array static unsigned int physicsManifoldsCount = 0; // Physics world current manifolds counter static Vector2 gravityForce = { 0.0f, 9.81f }; // Physics world gravity force // Utilities variables static unsigned int usedMemory = 0; // Total allocated dynamic memory //---------------------------------------------------------------------------------- // Module Internal Functions Declaration //---------------------------------------------------------------------------------- #if !defined(PHYSAC_AVOID_TIMMING_SYSTEM) // Timming measure functions static void InitTimerHiRes(void); // Initializes hi-resolution MONOTONIC timer static unsigned long long int GetClockTicks(void); // Get hi-res MONOTONIC time measure in mseconds static double GetCurrentTime(void); // Get current time measure in milliseconds #endif static void UpdatePhysicsStep(void); // Update physics step (dynamics, collisions and position corrections) static int FindAvailableBodyIndex(); // Finds a valid index for a new physics body initialization static int FindAvailableManifoldIndex(); // Finds a valid index for a new manifold initialization static PhysicsVertexData CreateDefaultPolygon(float radius, int sides); // Creates a random polygon shape with max vertex distance from polygon pivot static PhysicsVertexData CreateRectanglePolygon(Vector2 pos, Vector2 size); // Creates a rectangle polygon shape based on a min and max positions static void InitializePhysicsManifolds(PhysicsManifold manifold); // Initializes physics manifolds to solve collisions static PhysicsManifold CreatePhysicsManifold(PhysicsBody a, PhysicsBody b); // Creates a new physics manifold to solve collision static void DestroyPhysicsManifold(PhysicsManifold manifold); // Unitializes and destroys a physics manifold static void SolvePhysicsManifold(PhysicsManifold manifold); // Solves a created physics manifold between two physics bodies static void SolveCircleToCircle(PhysicsManifold manifold); // Solves collision between two circle shape physics bodies static void SolveCircleToPolygon(PhysicsManifold manifold); // Solves collision between a circle to a polygon shape physics bodies static void SolvePolygonToCircle(PhysicsManifold manifold); // Solves collision between a polygon to a circle shape physics bodies static void SolvePolygonToPolygon(PhysicsManifold manifold); // Solves collision between two polygons shape physics bodies static void IntegratePhysicsForces(PhysicsBody body); // Integrates physics forces into velocity static void IntegratePhysicsVelocity(PhysicsBody body); // Integrates physics velocity into position and forces static void IntegratePhysicsImpulses(PhysicsManifold manifold); // Integrates physics collisions impulses to solve collisions static void CorrectPhysicsPositions(PhysicsManifold manifold); // Corrects physics bodies positions based on manifolds collision information static void FindIncidentFace(Vector2 *v0, Vector2 *v1, PhysicsShape ref, PhysicsShape inc, int index); // Finds two polygon shapes incident face static float FindAxisLeastPenetration(int *faceIndex, PhysicsShape shapeA, PhysicsShape shapeB); // Finds polygon shapes axis least penetration // Math required functions static Vector2 MathVector2Product(Vector2 vector, float value); // Returns the product of a vector and a value static float MathVector2CrossProduct(Vector2 v1, Vector2 v2); // Returns the cross product of two vectors static float MathVector2SqrLen(Vector2 vector); // Returns the len square root of a vector static float MathVector2DotProduct(Vector2 v1, Vector2 v2); // Returns the dot product of two vectors static inline float MathVector2SqrDistance(Vector2 v1, Vector2 v2); // Returns the square root of distance between two vectors static void MathVector2Normalize(Vector2 *vector); // Returns the normalized values of a vector static Vector2 MathVector2Add(Vector2 v1, Vector2 v2); // Returns the sum of two given vectors static Vector2 MathVector2Subtract(Vector2 v1, Vector2 v2); // Returns the subtract of two given vectors static Matrix2x2 MathMatFromRadians(float radians); // Returns a matrix 2x2 from a given radians value static inline Matrix2x2 MathMatTranspose(Matrix2x2 matrix); // Returns the transpose of a given matrix 2x2 static inline Vector2 MathMatVector2Product(Matrix2x2 matrix, Vector2 vector); // Returns product between matrix 2x2 and vector static int MathVector2Clip(Vector2 normal, Vector2 *faceA, Vector2 *faceB, float clip); // Returns clipping value based on a normal and two faces static Vector2 MathTriangleBarycenter(Vector2 v1, Vector2 v2, Vector2 v3); // Returns the barycenter of a triangle given by 3 points //---------------------------------------------------------------------------------- // Module Functions Definition //---------------------------------------------------------------------------------- // Initializes physics values, pointers and creates physics loop thread void InitPhysics(void) { #if !defined(PHYSAC_AVOID_TIMMING_SYSTEM) // Initialize high resolution timer InitTimerHiRes(); #endif TRACELOG("[PHYSAC] Physics module initialized successfully\n"); } // Sets physics global gravity force void SetPhysicsGravity(float x, float y) { gravityForce.x = x; gravityForce.y = y; } // Creates a new circle physics body with generic parameters PhysicsBody CreatePhysicsBodyCircle(Vector2 pos, float radius, float density) { PhysicsBody body = CreatePhysicsBodyPolygon(pos, radius, PHYSAC_DEFAULT_CIRCLE_VERTICES, density); return body; } // Creates a new rectangle physics body with generic parameters PhysicsBody CreatePhysicsBodyRectangle(Vector2 pos, float width, float height, float density) { // NOTE: Make sure body data is initialized to 0 PhysicsBody body = (PhysicsBody)PHYSAC_CALLOC(sizeof(PhysicsBodyData), 1); usedMemory += sizeof(PhysicsBodyData); int id = FindAvailableBodyIndex(); if (id != -1) { // Initialize new body with generic values body->id = id; body->enabled = true; body->position = pos; body->shape.type = PHYSICS_POLYGON; body->shape.body = body; body->shape.transform = MathMatFromRadians(0.0f); body->shape.vertexData = CreateRectanglePolygon(pos, CLITERAL(Vector2){ width, height }); // Calculate centroid and moment of inertia Vector2 center = { 0.0f, 0.0f }; float area = 0.0f; float inertia = 0.0f; for (unsigned int i = 0; i < body->shape.vertexData.vertexCount; i++) { // Triangle vertices, third vertex implied as (0, 0) Vector2 p1 = body->shape.vertexData.positions[i]; unsigned int nextIndex = (((i + 1) < body->shape.vertexData.vertexCount) ? (i + 1) : 0); Vector2 p2 = body->shape.vertexData.positions[nextIndex]; float D = MathVector2CrossProduct(p1, p2); float triangleArea = D/2; area += triangleArea; // Use area to weight the centroid average, not just vertex position center.x += triangleArea*PHYSAC_K*(p1.x + p2.x); center.y += triangleArea*PHYSAC_K*(p1.y + p2.y); float intx2 = p1.x*p1.x + p2.x*p1.x + p2.x*p2.x; float inty2 = p1.y*p1.y + p2.y*p1.y + p2.y*p2.y; inertia += (0.25f*PHYSAC_K*D)*(intx2 + inty2); } center.x *= 1.0f/area; center.y *= 1.0f/area; // Translate vertices to centroid (make the centroid (0, 0) for the polygon in model space) // Note: this is not really necessary for (unsigned int i = 0; i < body->shape.vertexData.vertexCount; i++) { body->shape.vertexData.positions[i].x -= center.x; body->shape.vertexData.positions[i].y -= center.y; } body->mass = density*area; body->inverseMass = ((body->mass != 0.0f) ? 1.0f/body->mass : 0.0f); body->inertia = density*inertia; body->inverseInertia = ((body->inertia != 0.0f) ? 1.0f/body->inertia : 0.0f); body->staticFriction = 0.4f; body->dynamicFriction = 0.2f; body->restitution = 0.0f; body->useGravity = true; body->isGrounded = false; body->freezeOrient = false; // Add new body to bodies pointers array and update bodies count bodies[physicsBodiesCount] = body; physicsBodiesCount++; TRACELOG("[PHYSAC] Physic body created successfully (id: %i)\n", body->id); } else TRACELOG("[PHYSAC] Physic body could not be created, PHYSAC_MAX_BODIES reached\n"); return body; } // Creates a new polygon physics body with generic parameters PhysicsBody CreatePhysicsBodyPolygon(Vector2 pos, float radius, int sides, float density) { PhysicsBody body = (PhysicsBody)PHYSAC_MALLOC(sizeof(PhysicsBodyData)); usedMemory += sizeof(PhysicsBodyData); int id = FindAvailableBodyIndex(); if (id != -1) { // Initialize new body with generic values body->id = id; body->enabled = true; body->position = pos; body->velocity = PHYSAC_VECTOR_ZERO; body->force = PHYSAC_VECTOR_ZERO; body->angularVelocity = 0.0f; body->torque = 0.0f; body->orient = 0.0f; body->shape.type = PHYSICS_POLYGON; body->shape.body = body; body->shape.transform = MathMatFromRadians(0.0f); body->shape.vertexData = CreateDefaultPolygon(radius, sides); // Calculate centroid and moment of inertia Vector2 center = { 0.0f, 0.0f }; float area = 0.0f; float inertia = 0.0f; for (unsigned int i = 0; i < body->shape.vertexData.vertexCount; i++) { // Triangle vertices, third vertex implied as (0, 0) Vector2 position1 = body->shape.vertexData.positions[i]; unsigned int nextIndex = (((i + 1) < body->shape.vertexData.vertexCount) ? (i + 1) : 0); Vector2 position2 = body->shape.vertexData.positions[nextIndex]; float cross = MathVector2CrossProduct(position1, position2); float triangleArea = cross/2; area += triangleArea; // Use area to weight the centroid average, not just vertex position center.x += triangleArea*PHYSAC_K*(position1.x + position2.x); center.y += triangleArea*PHYSAC_K*(position1.y + position2.y); float intx2 = position1.x*position1.x + position2.x*position1.x + position2.x*position2.x; float inty2 = position1.y*position1.y + position2.y*position1.y + position2.y*position2.y; inertia += (0.25f*PHYSAC_K*cross)*(intx2 + inty2); } center.x *= 1.0f/area; center.y *= 1.0f/area; // Translate vertices to centroid (make the centroid (0, 0) for the polygon in model space) // Note: this is not really necessary for (unsigned int i = 0; i < body->shape.vertexData.vertexCount; i++) { body->shape.vertexData.positions[i].x -= center.x; body->shape.vertexData.positions[i].y -= center.y; } body->mass = density*area; body->inverseMass = ((body->mass != 0.0f) ? 1.0f/body->mass : 0.0f); body->inertia = density*inertia; body->inverseInertia = ((body->inertia != 0.0f) ? 1.0f/body->inertia : 0.0f); body->staticFriction = 0.4f; body->dynamicFriction = 0.2f; body->restitution = 0.0f; body->useGravity = true; body->isGrounded = false; body->freezeOrient = false; // Add new body to bodies pointers array and update bodies count bodies[physicsBodiesCount] = body; physicsBodiesCount++; TRACELOG("[PHYSAC] Physic body created successfully (id: %i)\n", body->id); } else TRACELOG("[PHYSAC] Physics body could not be created, PHYSAC_MAX_BODIES reached\n"); return body; } // Adds a force to a physics body void PhysicsAddForce(PhysicsBody body, Vector2 force) { if (body != NULL) body->force = MathVector2Add(body->force, force); } // Adds an angular force to a physics body void PhysicsAddTorque(PhysicsBody body, float amount) { if (body != NULL) body->torque += amount; } // Shatters a polygon shape physics body to little physics bodies with explosion force void PhysicsShatter(PhysicsBody body, Vector2 position, float force) { if (body != NULL) { if (body->shape.type == PHYSICS_POLYGON) { PhysicsVertexData vertexData = body->shape.vertexData; bool collision = false; for (unsigned int i = 0; i < vertexData.vertexCount; i++) { Vector2 positionA = body->position; Vector2 positionB = MathMatVector2Product(body->shape.transform, MathVector2Add(body->position, vertexData.positions[i])); unsigned int nextIndex = (((i + 1) < vertexData.vertexCount) ? (i + 1) : 0); Vector2 positionC = MathMatVector2Product(body->shape.transform, MathVector2Add(body->position, vertexData.positions[nextIndex])); // Check collision between each triangle float alpha = ((positionB.y - positionC.y)*(position.x - positionC.x) + (positionC.x - positionB.x)*(position.y - positionC.y))/ ((positionB.y - positionC.y)*(positionA.x - positionC.x) + (positionC.x - positionB.x)*(positionA.y - positionC.y)); float beta = ((positionC.y - positionA.y)*(position.x - positionC.x) + (positionA.x - positionC.x)*(position.y - positionC.y))/ ((positionB.y - positionC.y)*(positionA.x - positionC.x) + (positionC.x - positionB.x)*(positionA.y - positionC.y)); float gamma = 1.0f - alpha - beta; if ((alpha > 0.0f) && (beta > 0.0f) & (gamma > 0.0f)) { collision = true; break; } } if (collision) { int count = vertexData.vertexCount; Vector2 bodyPos = body->position; Vector2 *vertices = (Vector2 *)PHYSAC_MALLOC(sizeof(Vector2)*count); Matrix2x2 trans = body->shape.transform; for (int i = 0; i < count; i++) vertices[i] = vertexData.positions[i]; // Destroy shattered physics body DestroyPhysicsBody(body); for (int i = 0; i < count; i++) { int nextIndex = (((i + 1) < count) ? (i + 1) : 0); Vector2 center = MathTriangleBarycenter(vertices[i], vertices[nextIndex], PHYSAC_VECTOR_ZERO); center = MathVector2Add(bodyPos, center); Vector2 offset = MathVector2Subtract(center, bodyPos); PhysicsBody body = CreatePhysicsBodyPolygon(center, 10, 3, 10); // Create polygon physics body with relevant values PhysicsVertexData vertexData = { 0 }; vertexData.vertexCount = 3; vertexData.positions[0] = MathVector2Subtract(vertices[i], offset); vertexData.positions[1] = MathVector2Subtract(vertices[nextIndex], offset); vertexData.positions[2] = MathVector2Subtract(position, center); // Separate vertices to avoid unnecessary physics collisions vertexData.positions[0].x *= 0.95f; vertexData.positions[0].y *= 0.95f; vertexData.positions[1].x *= 0.95f; vertexData.positions[1].y *= 0.95f; vertexData.positions[2].x *= 0.95f; vertexData.positions[2].y *= 0.95f; // Calculate polygon faces normals for (unsigned int j = 0; j < vertexData.vertexCount; j++) { unsigned int nextVertex = (((j + 1) < vertexData.vertexCount) ? (j + 1) : 0); Vector2 face = MathVector2Subtract(vertexData.positions[nextVertex], vertexData.positions[j]); vertexData.normals[j] = CLITERAL(Vector2){ face.y, -face.x }; MathVector2Normalize(&vertexData.normals[j]); } // Apply computed vertex data to new physics body shape body->shape.vertexData = vertexData; body->shape.transform = trans; // Calculate centroid and moment of inertia center = PHYSAC_VECTOR_ZERO; float area = 0.0f; float inertia = 0.0f; for (unsigned int j = 0; j < body->shape.vertexData.vertexCount; j++) { // Triangle vertices, third vertex implied as (0, 0) Vector2 p1 = body->shape.vertexData.positions[j]; unsigned int nextVertex = (((j + 1) < body->shape.vertexData.vertexCount) ? (j + 1) : 0); Vector2 p2 = body->shape.vertexData.positions[nextVertex]; float D = MathVector2CrossProduct(p1, p2); float triangleArea = D/2; area += triangleArea; // Use area to weight the centroid average, not just vertex position center.x += triangleArea*PHYSAC_K*(p1.x + p2.x); center.y += triangleArea*PHYSAC_K*(p1.y + p2.y); float intx2 = p1.x*p1.x + p2.x*p1.x + p2.x*p2.x; float inty2 = p1.y*p1.y + p2.y*p1.y + p2.y*p2.y; inertia += (0.25f*PHYSAC_K*D)*(intx2 + inty2); } center.x *= 1.0f/area; center.y *= 1.0f/area; body->mass = area; body->inverseMass = ((body->mass != 0.0f) ? 1.0f/body->mass : 0.0f); body->inertia = inertia; body->inverseInertia = ((body->inertia != 0.0f) ? 1.0f/body->inertia : 0.0f); // Calculate explosion force direction Vector2 pointA = body->position; Vector2 pointB = MathVector2Subtract(vertexData.positions[1], vertexData.positions[0]); pointB.x /= 2.0f; pointB.y /= 2.0f; Vector2 forceDirection = MathVector2Subtract(MathVector2Add(pointA, MathVector2Add(vertexData.positions[0], pointB)), body->position); MathVector2Normalize(&forceDirection); forceDirection.x *= force; forceDirection.y *= force; // Apply force to new physics body PhysicsAddForce(body, forceDirection); } PHYSAC_FREE(vertices); } } } else TRACELOG("[PHYSAC] WARNING: PhysicsShatter: NULL physic body\n"); } // Returns the current amount of created physics bodies int GetPhysicsBodiesCount(void) { return physicsBodiesCount; } // Returns a physics body of the bodies pool at a specific index PhysicsBody GetPhysicsBody(int index) { PhysicsBody body = NULL; if (index < (int)physicsBodiesCount) { body = bodies[index]; if (body == NULL) TRACELOG("[PHYSAC] WARNING: GetPhysicsBody: NULL physic body\n"); } else TRACELOG("[PHYSAC] WARNING: Physic body index is out of bounds\n"); return body; } // Returns the physics body shape type (PHYSICS_CIRCLE or PHYSICS_POLYGON) int GetPhysicsShapeType(int index) { int result = -1; if (index < (int)physicsBodiesCount) { PhysicsBody body = bodies[index]; if (body != NULL) result = body->shape.type; else TRACELOG("[PHYSAC] WARNING: GetPhysicsShapeType: NULL physic body\n"); } else TRACELOG("[PHYSAC] WARNING: Physic body index is out of bounds\n"); return result; } // Returns the amount of vertices of a physics body shape int GetPhysicsShapeVerticesCount(int index) { int result = 0; if (index < (int)physicsBodiesCount) { PhysicsBody body = bodies[index]; if (body != NULL) { switch (body->shape.type) { case PHYSICS_CIRCLE: result = PHYSAC_DEFAULT_CIRCLE_VERTICES; break; case PHYSICS_POLYGON: result = body->shape.vertexData.vertexCount; break; default: break; } } else TRACELOG("[PHYSAC] WARNING: GetPhysicsShapeVerticesCount: NULL physic body\n"); } else TRACELOG("[PHYSAC] WARNING: Physic body index is out of bounds\n"); return result; } // Returns transformed position of a body shape (body position + vertex transformed position) Vector2 GetPhysicsShapeVertex(PhysicsBody body, int vertex) { Vector2 position = { 0.0f, 0.0f }; if (body != NULL) { switch (body->shape.type) { case PHYSICS_CIRCLE: { position.x = body->position.x + cosf(360.0f/PHYSAC_DEFAULT_CIRCLE_VERTICES*vertex*PHYSAC_DEG2RAD)*body->shape.radius; position.y = body->position.y + sinf(360.0f/PHYSAC_DEFAULT_CIRCLE_VERTICES*vertex*PHYSAC_DEG2RAD)*body->shape.radius; } break; case PHYSICS_POLYGON: { PhysicsVertexData vertexData = body->shape.vertexData; position = MathVector2Add(body->position, MathMatVector2Product(body->shape.transform, vertexData.positions[vertex])); } break; default: break; } } else TRACELOG("[PHYSAC] WARNING: GetPhysicsShapeVertex: NULL physic body\n"); return position; } // Sets physics body shape transform based on radians parameter void SetPhysicsBodyRotation(PhysicsBody body, float radians) { if (body != NULL) { body->orient = radians; if (body->shape.type == PHYSICS_POLYGON) body->shape.transform = MathMatFromRadians(radians); } } // Unitializes and destroys a physics body void DestroyPhysicsBody(PhysicsBody body) { if (body != NULL) { int id = body->id; int index = -1; for (unsigned int i = 0; i < physicsBodiesCount; i++) { if (bodies[i]->id == id) { index = i; break; } } if (index == -1) { TRACELOG("[PHYSAC] WARNING: Requested body (id: %i) can not be found\n", id); return; // Prevent access to index -1 } // Free body allocated memory PHYSAC_FREE(body); usedMemory -= sizeof(PhysicsBodyData); bodies[index] = NULL; // Reorder physics bodies pointers array and its catched index for (unsigned int i = index; i < physicsBodiesCount; i++) { if ((i + 1) < physicsBodiesCount) bodies[i] = bodies[i + 1]; } // Update physics bodies count physicsBodiesCount--; TRACELOG("[PHYSAC] Physic body destroyed successfully (id: %i)\n", id); } else TRACELOG("[PHYSAC] WARNING: DestroyPhysicsBody: NULL physic body\n"); } // Destroys created physics bodies and manifolds and resets global values void ResetPhysics(void) { if (physicsBodiesCount > 0) { // Unitialize physics bodies dynamic memory allocations for (int i = physicsBodiesCount - 1; i >= 0; i--) { PhysicsBody body = bodies[i]; if (body != NULL) { PHYSAC_FREE(body); bodies[i] = NULL; usedMemory -= sizeof(PhysicsBodyData); } } physicsBodiesCount = 0; } if (physicsManifoldsCount > 0) { // Unitialize physics manifolds dynamic memory allocations for (int i = physicsManifoldsCount - 1; i >= 0; i--) { PhysicsManifold manifold = contacts[i]; if (manifold != NULL) { PHYSAC_FREE(manifold); contacts[i] = NULL; usedMemory -= sizeof(PhysicsManifoldData); } } physicsManifoldsCount = 0; } TRACELOG("[PHYSAC] Physics module reseted successfully\n"); } // Unitializes physics pointers and exits physics loop thread void ClosePhysics(void) { // Unitialize physics manifolds dynamic memory allocations if (physicsManifoldsCount > 0) { for (int i = physicsManifoldsCount - 1; i >= 0; i--) DestroyPhysicsManifold(contacts[i]); } // Unitialize physics bodies dynamic memory allocations if (physicsBodiesCount > 0) { for (int i = physicsBodiesCount - 1; i >= 0; i--) DestroyPhysicsBody(bodies[i]); } // Trace log info if ((physicsBodiesCount > 0) || (usedMemory != 0)) { TRACELOG("[PHYSAC] WARNING: Physics module closed with unallocated bodies (BODIES: %i, MEMORY: %i bytes)\n", physicsBodiesCount, usedMemory); } else if ((physicsManifoldsCount > 0) || (usedMemory != 0)) { TRACELOG("[PHYSAC] WARNING: Pysics module closed with unallocated manifolds (MANIFOLDS: %i, MEMORY: %i bytes)\n", physicsManifoldsCount, usedMemory); } else TRACELOG("[PHYSAC] Physics module closed successfully\n"); } // Update physics system // Physics steps are launched at a fixed time step if enabled void UpdatePhysics(void) { #if !defined(PHYSAC_AVOID_TIMMING_SYSTEM) static double deltaTimeAccumulator = 0.0; // Calculate current time (ms) currentTime = GetCurrentTime(); // Calculate current delta time (ms) const double delta = currentTime - startTime; // Store the time elapsed since the last frame began deltaTimeAccumulator += delta; // Fixed time stepping loop while (deltaTimeAccumulator >= deltaTime) { UpdatePhysicsStep(); deltaTimeAccumulator -= deltaTime; } // Record the starting of this frame startTime = currentTime; #else UpdatePhysicsStep(); #endif } void SetPhysicsTimeStep(double delta) { deltaTime = delta; } //---------------------------------------------------------------------------------- // Module Internal Functions Definition //---------------------------------------------------------------------------------- #if !defined(PHYSAC_AVOID_TIMMING_SYSTEM) // Initializes hi-resolution MONOTONIC timer static void InitTimerHiRes(void) { #if defined(_WIN32) QueryPerformanceFrequency((unsigned long long int *) &frequency); #endif #if defined(__EMSCRIPTEN__) || defined(__linux__) struct timespec now; if (clock_gettime(CLOCK_MONOTONIC, &now) == 0) frequency = 1000000000; #endif #if defined(__APPLE__) mach_timebase_info_data_t timebase; mach_timebase_info(&timebase); frequency = (timebase.denom*1e9)/timebase.numer; #endif baseClockTicks = (double)GetClockTicks(); // Get MONOTONIC clock time offset startTime = GetCurrentTime(); // Get current time in milliseconds } // Get hi-res MONOTONIC time measure in clock ticks static unsigned long long int GetClockTicks(void) { unsigned long long int value = 0; #if defined(_WIN32) QueryPerformanceCounter((unsigned long long int *) &value); #endif #if defined(__linux__) struct timespec now; clock_gettime(CLOCK_MONOTONIC, &now); value = (unsigned long long int)now.tv_sec*(unsigned long long int)1000000000 + (unsigned long long int)now.tv_nsec; #endif #if defined(__APPLE__) value = mach_absolute_time(); #endif return value; } // Get current time in milliseconds static double GetCurrentTime(void) { return (double)(GetClockTicks() - baseClockTicks)/frequency*1000; } #endif // !PHYSAC_AVOID_TIMMING_SYSTEM // Update physics step (dynamics, collisions and position corrections) static void UpdatePhysicsStep(void) { // Clear previous generated collisions information for (int i = (int)physicsManifoldsCount - 1; i >= 0; i--) { PhysicsManifold manifold = contacts[i]; if (manifold != NULL) DestroyPhysicsManifold(manifold); } // Reset physics bodies grounded state for (unsigned int i = 0; i < physicsBodiesCount; i++) { PhysicsBody body = bodies[i]; body->isGrounded = false; } // Generate new collision information for (unsigned int i = 0; i < physicsBodiesCount; i++) { PhysicsBody bodyA = bodies[i]; if (bodyA != NULL) { for (unsigned int j = i + 1; j < physicsBodiesCount; j++) { PhysicsBody bodyB = bodies[j]; if (bodyB != NULL) { if ((bodyA->inverseMass == 0) && (bodyB->inverseMass == 0)) continue; PhysicsManifold manifold = CreatePhysicsManifold(bodyA, bodyB); SolvePhysicsManifold(manifold); if (manifold->contactsCount > 0) { // Create a new manifold with same information as previously solved manifold and add it to the manifolds pool last slot PhysicsManifold manifold = CreatePhysicsManifold(bodyA, bodyB); manifold->penetration = manifold->penetration; manifold->normal = manifold->normal; manifold->contacts[0] = manifold->contacts[0]; manifold->contacts[1] = manifold->contacts[1]; manifold->contactsCount = manifold->contactsCount; manifold->restitution = manifold->restitution; manifold->dynamicFriction = manifold->dynamicFriction; manifold->staticFriction = manifold->staticFriction; } } } } } // Integrate forces to physics bodies for (unsigned int i = 0; i < physicsBodiesCount; i++) { PhysicsBody body = bodies[i]; if (body != NULL) IntegratePhysicsForces(body); } // Initialize physics manifolds to solve collisions for (unsigned int i = 0; i < physicsManifoldsCount; i++) { PhysicsManifold manifold = contacts[i]; if (manifold != NULL) InitializePhysicsManifolds(manifold); } // Integrate physics collisions impulses to solve collisions for (unsigned int i = 0; i < PHYSAC_COLLISION_ITERATIONS; i++) { for (unsigned int j = 0; j < physicsManifoldsCount; j++) { PhysicsManifold manifold = contacts[i]; if (manifold != NULL) IntegratePhysicsImpulses(manifold); } } // Integrate velocity to physics bodies for (unsigned int i = 0; i < physicsBodiesCount; i++) { PhysicsBody body = bodies[i]; if (body != NULL) IntegratePhysicsVelocity(body); } // Correct physics bodies positions based on manifolds collision information for (unsigned int i = 0; i < physicsManifoldsCount; i++) { PhysicsManifold manifold = contacts[i]; if (manifold != NULL) CorrectPhysicsPositions(manifold); } // Clear physics bodies forces for (unsigned int i = 0; i < physicsBodiesCount; i++) { PhysicsBody body = bodies[i]; if (body != NULL) { body->force = PHYSAC_VECTOR_ZERO; body->torque = 0.0f; } } } // Finds a valid index for a new physics body initialization static int FindAvailableBodyIndex() { int index = -1; for (int i = 0; i < PHYSAC_MAX_BODIES; i++) { int currentId = i; // Check if current id already exist in other physics body for (unsigned int k = 0; k < physicsBodiesCount; k++) { if (bodies[k]->id == currentId) { currentId++; break; } } // If it is not used, use it as new physics body id if (currentId == (int)i) { index = (int)i; break; } } return index; } // Creates a default polygon shape with max vertex distance from polygon pivot static PhysicsVertexData CreateDefaultPolygon(float radius, int sides) { PhysicsVertexData data = { 0 }; data.vertexCount = sides; // Calculate polygon vertices positions for (unsigned int i = 0; i < data.vertexCount; i++) { data.positions[i].x = (float)cosf(360.0f/sides*i*PHYSAC_DEG2RAD)*radius; data.positions[i].y = (float)sinf(360.0f/sides*i*PHYSAC_DEG2RAD)*radius; } // Calculate polygon faces normals for (int i = 0; i < (int)data.vertexCount; i++) { int nextIndex = (((i + 1) < sides) ? (i + 1) : 0); Vector2 face = MathVector2Subtract(data.positions[nextIndex], data.positions[i]); data.normals[i] = CLITERAL(Vector2){ face.y, -face.x }; MathVector2Normalize(&data.normals[i]); } return data; } // Creates a rectangle polygon shape based on a min and max positions static PhysicsVertexData CreateRectanglePolygon(Vector2 pos, Vector2 size) { PhysicsVertexData data = { 0 }; data.vertexCount = 4; // Calculate polygon vertices positions data.positions[0] = CLITERAL(Vector2){ pos.x + size.x/2, pos.y - size.y/2 }; data.positions[1] = CLITERAL(Vector2){ pos.x + size.x/2, pos.y + size.y/2 }; data.positions[2] = CLITERAL(Vector2){ pos.x - size.x/2, pos.y + size.y/2 }; data.positions[3] = CLITERAL(Vector2){ pos.x - size.x/2, pos.y - size.y/2 }; // Calculate polygon faces normals for (unsigned int i = 0; i < data.vertexCount; i++) { int nextIndex = (((i + 1) < data.vertexCount) ? (i + 1) : 0); Vector2 face = MathVector2Subtract(data.positions[nextIndex], data.positions[i]); data.normals[i] = CLITERAL(Vector2){ face.y, -face.x }; MathVector2Normalize(&data.normals[i]); } return data; } // Finds a valid index for a new manifold initialization static int FindAvailableManifoldIndex() { int index = -1; for (int i = 0; i < PHYSAC_MAX_MANIFOLDS; i++) { int currentId = i; // Check if current id already exist in other physics body for (unsigned int k = 0; k < physicsManifoldsCount; k++) { if (contacts[k]->id == currentId) { currentId++; break; } } // If it is not used, use it as new physics body id if (currentId == i) { index = i; break; } } return index; } // Creates a new physics manifold to solve collision static PhysicsManifold CreatePhysicsManifold(PhysicsBody a, PhysicsBody b) { PhysicsManifold manifold = (PhysicsManifold)PHYSAC_MALLOC(sizeof(PhysicsManifoldData)); usedMemory += sizeof(PhysicsManifoldData); int id = FindAvailableManifoldIndex(); if (id != -1) { // Initialize new manifold with generic values manifold->id = id; manifold->bodyA = a; manifold->bodyB = b; manifold->penetration = 0; manifold->normal = PHYSAC_VECTOR_ZERO; manifold->contacts[0] = PHYSAC_VECTOR_ZERO; manifold->contacts[1] = PHYSAC_VECTOR_ZERO; manifold->contactsCount = 0; manifold->restitution = 0.0f; manifold->dynamicFriction = 0.0f; manifold->staticFriction = 0.0f; // Add new body to bodies pointers array and update bodies count contacts[physicsManifoldsCount] = manifold; physicsManifoldsCount++; } else TRACELOG("[PHYSAC] Physic manifold could not be created, PHYSAC_MAX_MANIFOLDS reached\n"); return manifold; } // Unitializes and destroys a physics manifold static void DestroyPhysicsManifold(PhysicsManifold manifold) { if (manifold != NULL) { int id = manifold->id; int index = -1; for (unsigned int i = 0; i < physicsManifoldsCount; i++) { if (contacts[i]->id == id) { index = i; break; } } if (index == -1) return; // Prevent access to index -1 // Free manifold allocated memory PHYSAC_FREE(manifold); usedMemory -= sizeof(PhysicsManifoldData); contacts[index] = NULL; // Reorder physics manifolds pointers array and its catched index for (unsigned int i = index; i < physicsManifoldsCount; i++) { if ((i + 1) < physicsManifoldsCount) contacts[i] = contacts[i + 1]; } // Update physics manifolds count physicsManifoldsCount--; } else TRACELOG("[PHYSAC] WARNING: DestroyPhysicsManifold: NULL physic manifold\n"); } // Solves a created physics manifold between two physics bodies static void SolvePhysicsManifold(PhysicsManifold manifold) { switch (manifold->bodyA->shape.type) { case PHYSICS_CIRCLE: { switch (manifold->bodyB->shape.type) { case PHYSICS_CIRCLE: SolveCircleToCircle(manifold); break; case PHYSICS_POLYGON: SolveCircleToPolygon(manifold); break; default: break; } } break; case PHYSICS_POLYGON: { switch (manifold->bodyB->shape.type) { case PHYSICS_CIRCLE: SolvePolygonToCircle(manifold); break; case PHYSICS_POLYGON: SolvePolygonToPolygon(manifold); break; default: break; } } break; default: break; } // Update physics body grounded state if normal direction is down and grounded state is not set yet in previous manifolds if (!manifold->bodyB->isGrounded) manifold->bodyB->isGrounded = (manifold->normal.y < 0); } // Solves collision between two circle shape physics bodies static void SolveCircleToCircle(PhysicsManifold manifold) { PhysicsBody bodyA = manifold->bodyA; PhysicsBody bodyB = manifold->bodyB; if ((bodyA == NULL) || (bodyB == NULL)) return; // Calculate translational vector, which is normal Vector2 normal = MathVector2Subtract(bodyB->position, bodyA->position); float distSqr = MathVector2SqrLen(normal); float radius = bodyA->shape.radius + bodyB->shape.radius; // Check if circles are not in contact if (distSqr >= radius*radius) { manifold->contactsCount = 0; return; } float distance = sqrtf(distSqr); manifold->contactsCount = 1; if (distance == 0.0f) { manifold->penetration = bodyA->shape.radius; manifold->normal = CLITERAL(Vector2){ 1.0f, 0.0f }; manifold->contacts[0] = bodyA->position; } else { manifold->penetration = radius - distance; manifold->normal = CLITERAL(Vector2){ normal.x/distance, normal.y/distance }; // Faster than using MathVector2Normalize() due to sqrt is already performed manifold->contacts[0] = CLITERAL(Vector2){ manifold->normal.x*bodyA->shape.radius + bodyA->position.x, manifold->normal.y*bodyA->shape.radius + bodyA->position.y }; } // Update physics body grounded state if normal direction is down if (!bodyA->isGrounded) bodyA->isGrounded = (manifold->normal.y < 0); } // Solves collision between a circle to a polygon shape physics bodies static void SolveCircleToPolygon(PhysicsManifold manifold) { PhysicsBody bodyA = manifold->bodyA; PhysicsBody bodyB = manifold->bodyB; if ((bodyA == NULL) || (bodyB == NULL)) return; manifold->contactsCount = 0; // Transform circle center to polygon transform space Vector2 center = bodyA->position; center = MathMatVector2Product(MathMatTranspose(bodyB->shape.transform), MathVector2Subtract(center, bodyB->position)); // Find edge with minimum penetration // It is the same concept as using support points in SolvePolygonToPolygon float separation = -PHYSAC_FLT_MAX; int faceNormal = 0; PhysicsVertexData vertexData = bodyB->shape.vertexData; for (unsigned int i = 0; i < vertexData.vertexCount; i++) { float currentSeparation = MathVector2DotProduct(vertexData.normals[i], MathVector2Subtract(center, vertexData.positions[i])); if (currentSeparation > bodyA->shape.radius) return; if (currentSeparation > separation) { separation = currentSeparation; faceNormal = i; } } // Grab face's vertices Vector2 v1 = vertexData.positions[faceNormal]; int nextIndex = (((faceNormal + 1) < (int)vertexData.vertexCount) ? (faceNormal + 1) : 0); Vector2 v2 = vertexData.positions[nextIndex]; // Check to see if center is within polygon if (separation < PHYSAC_EPSILON) { manifold->contactsCount = 1; Vector2 normal = MathMatVector2Product(bodyB->shape.transform, vertexData.normals[faceNormal]); manifold->normal = CLITERAL(Vector2){ -normal.x, -normal.y }; manifold->contacts[0] = CLITERAL(Vector2){ manifold->normal.x*bodyA->shape.radius + bodyA->position.x, manifold->normal.y*bodyA->shape.radius + bodyA->position.y }; manifold->penetration = bodyA->shape.radius; return; } // Determine which voronoi region of the edge center of circle lies within float dot1 = MathVector2DotProduct(MathVector2Subtract(center, v1), MathVector2Subtract(v2, v1)); float dot2 = MathVector2DotProduct(MathVector2Subtract(center, v2), MathVector2Subtract(v1, v2)); manifold->penetration = bodyA->shape.radius - separation; if (dot1 <= 0.0f) // Closest to v1 { if (MathVector2SqrDistance(center, v1) > bodyA->shape.radius*bodyA->shape.radius) return; manifold->contactsCount = 1; Vector2 normal = MathVector2Subtract(v1, center); normal = MathMatVector2Product(bodyB->shape.transform, normal); MathVector2Normalize(&normal); manifold->normal = normal; v1 = MathMatVector2Product(bodyB->shape.transform, v1); v1 = MathVector2Add(v1, bodyB->position); manifold->contacts[0] = v1; } else if (dot2 <= 0.0f) // Closest to v2 { if (MathVector2SqrDistance(center, v2) > bodyA->shape.radius*bodyA->shape.radius) return; manifold->contactsCount = 1; Vector2 normal = MathVector2Subtract(v2, center); v2 = MathMatVector2Product(bodyB->shape.transform, v2); v2 = MathVector2Add(v2, bodyB->position); manifold->contacts[0] = v2; normal = MathMatVector2Product(bodyB->shape.transform, normal); MathVector2Normalize(&normal); manifold->normal = normal; } else // Closest to face { Vector2 normal = vertexData.normals[faceNormal]; if (MathVector2DotProduct(MathVector2Subtract(center, v1), normal) > bodyA->shape.radius) return; normal = MathMatVector2Product(bodyB->shape.transform, normal); manifold->normal = CLITERAL(Vector2){ -normal.x, -normal.y }; manifold->contacts[0] = CLITERAL(Vector2){ manifold->normal.x*bodyA->shape.radius + bodyA->position.x, manifold->normal.y*bodyA->shape.radius + bodyA->position.y }; manifold->contactsCount = 1; } } // Solves collision between a polygon to a circle shape physics bodies static void SolvePolygonToCircle(PhysicsManifold manifold) { PhysicsBody bodyA = manifold->bodyA; PhysicsBody bodyB = manifold->bodyB; if ((bodyA == NULL) || (bodyB == NULL)) return; manifold->bodyA = bodyB; manifold->bodyB = bodyA; SolveCircleToPolygon(manifold); manifold->normal.x *= -1.0f; manifold->normal.y *= -1.0f; } // Solves collision between two polygons shape physics bodies static void SolvePolygonToPolygon(PhysicsManifold manifold) { if ((manifold->bodyA == NULL) || (manifold->bodyB == NULL)) return; PhysicsShape bodyA = manifold->bodyA->shape; PhysicsShape bodyB = manifold->bodyB->shape; manifold->contactsCount = 0; // Check for separating axis with A shape's face planes int faceA = 0; float penetrationA = FindAxisLeastPenetration(&faceA, bodyA, bodyB); if (penetrationA >= 0.0f) return; // Check for separating axis with B shape's face planes int faceB = 0; float penetrationB = FindAxisLeastPenetration(&faceB, bodyB, bodyA); if (penetrationB >= 0.0f) return; int referenceIndex = 0; bool flip = false; // Always point from A shape to B shape PhysicsShape refPoly; // Reference PhysicsShape incPoly; // Incident // Determine which shape contains reference face // Checking bias range for penetration if (penetrationA >= (penetrationB*0.95f + penetrationA*0.01f)) { refPoly = bodyA; incPoly = bodyB; referenceIndex = faceA; } else { refPoly = bodyB; incPoly = bodyA; referenceIndex = faceB; flip = true; } // World space incident face Vector2 incidentFace[2]; FindIncidentFace(&incidentFace[0], &incidentFace[1], refPoly, incPoly, referenceIndex); // Setup reference face vertices PhysicsVertexData refData = refPoly.vertexData; Vector2 v1 = refData.positions[referenceIndex]; referenceIndex = (((referenceIndex + 1) < (int)refData.vertexCount) ? (referenceIndex + 1) : 0); Vector2 v2 = refData.positions[referenceIndex]; // Transform vertices to world space v1 = MathMatVector2Product(refPoly.transform, v1); v1 = MathVector2Add(v1, refPoly.body->position); v2 = MathMatVector2Product(refPoly.transform, v2); v2 = MathVector2Add(v2, refPoly.body->position); // Calculate reference face side normal in world space Vector2 sidePlaneNormal = MathVector2Subtract(v2, v1); MathVector2Normalize(&sidePlaneNormal); // Orthogonalize Vector2 refFaceNormal = { sidePlaneNormal.y, -sidePlaneNormal.x }; float refC = MathVector2DotProduct(refFaceNormal, v1); float negSide = MathVector2DotProduct(sidePlaneNormal, v1)*-1; float posSide = MathVector2DotProduct(sidePlaneNormal, v2); // MathVector2Clip incident face to reference face side planes (due to floating point error, possible to not have required points if (MathVector2Clip(CLITERAL(Vector2){ -sidePlaneNormal.x, -sidePlaneNormal.y }, &incidentFace[0], &incidentFace[1], negSide) < 2) return; if (MathVector2Clip(sidePlaneNormal, &incidentFace[0], &incidentFace[1], posSide) < 2) return; // Flip normal if required manifold->normal = (flip ? CLITERAL(Vector2){ -refFaceNormal.x, -refFaceNormal.y } : refFaceNormal); // Keep points behind reference face int currentPoint = 0; // MathVector2Clipped points behind reference face float separation = MathVector2DotProduct(refFaceNormal, incidentFace[0]) - refC; if (separation <= 0.0f) { manifold->contacts[currentPoint] = incidentFace[0]; manifold->penetration = -separation; currentPoint++; } else manifold->penetration = 0.0f; separation = MathVector2DotProduct(refFaceNormal, incidentFace[1]) - refC; if (separation <= 0.0f) { manifold->contacts[currentPoint] = incidentFace[1]; manifold->penetration += -separation; currentPoint++; // Calculate total penetration average manifold->penetration /= currentPoint; } manifold->contactsCount = currentPoint; } // Integrates physics forces into velocity static void IntegratePhysicsForces(PhysicsBody body) { if ((body == NULL) || (body->inverseMass == 0.0f) || !body->enabled) return; body->velocity.x += (float)((body->force.x*body->inverseMass)*(deltaTime/2.0)); body->velocity.y += (float)((body->force.y*body->inverseMass)*(deltaTime/2.0)); if (body->useGravity) { body->velocity.x += (float)(gravityForce.x*(deltaTime/1000/2.0)); body->velocity.y += (float)(gravityForce.y*(deltaTime/1000/2.0)); } if (!body->freezeOrient) body->angularVelocity += (float)(body->torque*body->inverseInertia*(deltaTime/2.0)); } // Initializes physics manifolds to solve collisions static void InitializePhysicsManifolds(PhysicsManifold manifold) { PhysicsBody bodyA = manifold->bodyA; PhysicsBody bodyB = manifold->bodyB; if ((bodyA == NULL) || (bodyB == NULL)) return; // Calculate average restitution, static and dynamic friction manifold->restitution = sqrtf(bodyA->restitution*bodyB->restitution); manifold->staticFriction = sqrtf(bodyA->staticFriction*bodyB->staticFriction); manifold->dynamicFriction = sqrtf(bodyA->dynamicFriction*bodyB->dynamicFriction); for (unsigned int i = 0; i < manifold->contactsCount; i++) { // Caculate radius from center of mass to contact Vector2 radiusA = MathVector2Subtract(manifold->contacts[i], bodyA->position); Vector2 radiusB = MathVector2Subtract(manifold->contacts[i], bodyB->position); Vector2 crossA = MathVector2Product(radiusA, bodyA->angularVelocity); Vector2 crossB = MathVector2Product(radiusB, bodyB->angularVelocity); Vector2 radiusV = { 0.0f, 0.0f }; radiusV.x = bodyB->velocity.x + crossB.x - bodyA->velocity.x - crossA.x; radiusV.y = bodyB->velocity.y + crossB.y - bodyA->velocity.y - crossA.y; // Determine if we should perform a resting collision or not; // The idea is if the only thing moving this object is gravity, then the collision should be performed without any restitution if (MathVector2SqrLen(radiusV) < (MathVector2SqrLen(CLITERAL(Vector2){ (float)(gravityForce.x*deltaTime/1000), (float)(gravityForce.y*deltaTime/1000) }) + PHYSAC_EPSILON)) manifold->restitution = 0; } } // Integrates physics collisions impulses to solve collisions static void IntegratePhysicsImpulses(PhysicsManifold manifold) { PhysicsBody bodyA = manifold->bodyA; PhysicsBody bodyB = manifold->bodyB; if ((bodyA == NULL) || (bodyB == NULL)) return; // Early out and positional correct if both objects have infinite mass if (fabs(bodyA->inverseMass + bodyB->inverseMass) <= PHYSAC_EPSILON) { bodyA->velocity = PHYSAC_VECTOR_ZERO; bodyB->velocity = PHYSAC_VECTOR_ZERO; return; } for (unsigned int i = 0; i < manifold->contactsCount; i++) { // Calculate radius from center of mass to contact Vector2 radiusA = MathVector2Subtract(manifold->contacts[i], bodyA->position); Vector2 radiusB = MathVector2Subtract(manifold->contacts[i], bodyB->position); // Calculate relative velocity Vector2 radiusV = { 0.0f, 0.0f }; radiusV.x = bodyB->velocity.x + MathVector2Product(radiusB, bodyB->angularVelocity).x - bodyA->velocity.x - MathVector2Product(radiusA, bodyA->angularVelocity).x; radiusV.y = bodyB->velocity.y + MathVector2Product(radiusB, bodyB->angularVelocity).y - bodyA->velocity.y - MathVector2Product(radiusA, bodyA->angularVelocity).y; // Relative velocity along the normal float contactVelocity = MathVector2DotProduct(radiusV, manifold->normal); // Do not resolve if velocities are separating if (contactVelocity > 0.0f) return; float raCrossN = MathVector2CrossProduct(radiusA, manifold->normal); float rbCrossN = MathVector2CrossProduct(radiusB, manifold->normal); float inverseMassSum = bodyA->inverseMass + bodyB->inverseMass + (raCrossN*raCrossN)*bodyA->inverseInertia + (rbCrossN*rbCrossN)*bodyB->inverseInertia; // Calculate impulse scalar value float impulse = -(1.0f + manifold->restitution)*contactVelocity; impulse /= inverseMassSum; impulse /= (float)manifold->contactsCount; // Apply impulse to each physics body Vector2 impulseV = { manifold->normal.x*impulse, manifold->normal.y*impulse }; if (bodyA->enabled) { bodyA->velocity.x += bodyA->inverseMass*(-impulseV.x); bodyA->velocity.y += bodyA->inverseMass*(-impulseV.y); if (!bodyA->freezeOrient) bodyA->angularVelocity += bodyA->inverseInertia*MathVector2CrossProduct(radiusA, CLITERAL(Vector2){ -impulseV.x, -impulseV.y }); } if (bodyB->enabled) { bodyB->velocity.x += bodyB->inverseMass*(impulseV.x); bodyB->velocity.y += bodyB->inverseMass*(impulseV.y); if (!bodyB->freezeOrient) bodyB->angularVelocity += bodyB->inverseInertia*MathVector2CrossProduct(radiusB, impulseV); } // Apply friction impulse to each physics body radiusV.x = bodyB->velocity.x + MathVector2Product(radiusB, bodyB->angularVelocity).x - bodyA->velocity.x - MathVector2Product(radiusA, bodyA->angularVelocity).x; radiusV.y = bodyB->velocity.y + MathVector2Product(radiusB, bodyB->angularVelocity).y - bodyA->velocity.y - MathVector2Product(radiusA, bodyA->angularVelocity).y; Vector2 tangent = { radiusV.x - (manifold->normal.x*MathVector2DotProduct(radiusV, manifold->normal)), radiusV.y - (manifold->normal.y*MathVector2DotProduct(radiusV, manifold->normal)) }; MathVector2Normalize(&tangent); // Calculate impulse tangent magnitude float impulseTangent = -MathVector2DotProduct(radiusV, tangent); impulseTangent /= inverseMassSum; impulseTangent /= (float)manifold->contactsCount; float absImpulseTangent = (float)fabs(impulseTangent); // Don't apply tiny friction impulses if (absImpulseTangent <= PHYSAC_EPSILON) return; // Apply coulumb's law Vector2 tangentImpulse = { 0.0f, 0.0f }; if (absImpulseTangent < impulse*manifold->staticFriction) tangentImpulse = CLITERAL(Vector2){ tangent.x*impulseTangent, tangent.y*impulseTangent }; else tangentImpulse = CLITERAL(Vector2){ tangent.x*-impulse*manifold->dynamicFriction, tangent.y*-impulse*manifold->dynamicFriction }; // Apply friction impulse if (bodyA->enabled) { bodyA->velocity.x += bodyA->inverseMass*(-tangentImpulse.x); bodyA->velocity.y += bodyA->inverseMass*(-tangentImpulse.y); if (!bodyA->freezeOrient) bodyA->angularVelocity += bodyA->inverseInertia*MathVector2CrossProduct(radiusA, CLITERAL(Vector2){ -tangentImpulse.x, -tangentImpulse.y }); } if (bodyB->enabled) { bodyB->velocity.x += bodyB->inverseMass*(tangentImpulse.x); bodyB->velocity.y += bodyB->inverseMass*(tangentImpulse.y); if (!bodyB->freezeOrient) bodyB->angularVelocity += bodyB->inverseInertia*MathVector2CrossProduct(radiusB, tangentImpulse); } } } // Integrates physics velocity into position and forces static void IntegratePhysicsVelocity(PhysicsBody body) { if ((body == NULL) ||!body->enabled) return; body->position.x += (float)(body->velocity.x*deltaTime); body->position.y += (float)(body->velocity.y*deltaTime); if (!body->freezeOrient) body->orient += (float)(body->angularVelocity*deltaTime); body->shape.transform = MathMatFromRadians(body->orient); IntegratePhysicsForces(body); } // Corrects physics bodies positions based on manifolds collision information static void CorrectPhysicsPositions(PhysicsManifold manifold) { PhysicsBody bodyA = manifold->bodyA; PhysicsBody bodyB = manifold->bodyB; if ((bodyA == NULL) || (bodyB == NULL)) return; Vector2 correction = { 0.0f, 0.0f }; correction.x = (PHYSAC_MAX(manifold->penetration - PHYSAC_PENETRATION_ALLOWANCE, 0.0f)/(bodyA->inverseMass + bodyB->inverseMass))*manifold->normal.x*PHYSAC_PENETRATION_CORRECTION; correction.y = (PHYSAC_MAX(manifold->penetration - PHYSAC_PENETRATION_ALLOWANCE, 0.0f)/(bodyA->inverseMass + bodyB->inverseMass))*manifold->normal.y*PHYSAC_PENETRATION_CORRECTION; if (bodyA->enabled) { bodyA->position.x -= correction.x*bodyA->inverseMass; bodyA->position.y -= correction.y*bodyA->inverseMass; } if (bodyB->enabled) { bodyB->position.x += correction.x*bodyB->inverseMass; bodyB->position.y += correction.y*bodyB->inverseMass; } } // Returns the extreme point along a direction within a polygon static Vector2 GetSupport(PhysicsShape shape, Vector2 dir) { float bestProjection = -PHYSAC_FLT_MAX; Vector2 bestVertex = { 0.0f, 0.0f }; PhysicsVertexData data = shape.vertexData; for (unsigned int i = 0; i < data.vertexCount; i++) { Vector2 vertex = data.positions[i]; float projection = MathVector2DotProduct(vertex, dir); if (projection > bestProjection) { bestVertex = vertex; bestProjection = projection; } } return bestVertex; } // Finds polygon shapes axis least penetration static float FindAxisLeastPenetration(int *faceIndex, PhysicsShape shapeA, PhysicsShape shapeB) { float bestDistance = -PHYSAC_FLT_MAX; int bestIndex = 0; PhysicsVertexData dataA = shapeA.vertexData; //PhysicsVertexData dataB = shapeB.vertexData; for (unsigned int i = 0; i < dataA.vertexCount; i++) { // Retrieve a face normal from A shape Vector2 normal = dataA.normals[i]; Vector2 transNormal = MathMatVector2Product(shapeA.transform, normal); // Transform face normal into B shape's model space Matrix2x2 buT = MathMatTranspose(shapeB.transform); normal = MathMatVector2Product(buT, transNormal); // Retrieve support point from B shape along -n Vector2 support = GetSupport(shapeB, CLITERAL(Vector2){ -normal.x, -normal.y }); // Retrieve vertex on face from A shape, transform into B shape's model space Vector2 vertex = dataA.positions[i]; vertex = MathMatVector2Product(shapeA.transform, vertex); vertex = MathVector2Add(vertex, shapeA.body->position); vertex = MathVector2Subtract(vertex, shapeB.body->position); vertex = MathMatVector2Product(buT, vertex); // Compute penetration distance in B shape's model space float distance = MathVector2DotProduct(normal, MathVector2Subtract(support, vertex)); // Store greatest distance if (distance > bestDistance) { bestDistance = distance; bestIndex = i; } } *faceIndex = bestIndex; return bestDistance; } // Finds two polygon shapes incident face static void FindIncidentFace(Vector2 *v0, Vector2 *v1, PhysicsShape ref, PhysicsShape inc, int index) { PhysicsVertexData refData = ref.vertexData; PhysicsVertexData incData = inc.vertexData; Vector2 referenceNormal = refData.normals[index]; // Calculate normal in incident's frame of reference referenceNormal = MathMatVector2Product(ref.transform, referenceNormal); // To world space referenceNormal = MathMatVector2Product(MathMatTranspose(inc.transform), referenceNormal); // To incident's model space // Find most anti-normal face on polygon int incidentFace = 0; float minDot = PHYSAC_FLT_MAX; for (unsigned int i = 0; i < incData.vertexCount; i++) { float dot = MathVector2DotProduct(referenceNormal, incData.normals[i]); if (dot < minDot) { minDot = dot; incidentFace = i; } } // Assign face vertices for incident face *v0 = MathMatVector2Product(inc.transform, incData.positions[incidentFace]); *v0 = MathVector2Add(*v0, inc.body->position); incidentFace = (((incidentFace + 1) < (int)incData.vertexCount) ? (incidentFace + 1) : 0); *v1 = MathMatVector2Product(inc.transform, incData.positions[incidentFace]); *v1 = MathVector2Add(*v1, inc.body->position); } // Returns clipping value based on a normal and two faces static int MathVector2Clip(Vector2 normal, Vector2 *faceA, Vector2 *faceB, float clip) { int sp = 0; Vector2 out[2] = { *faceA, *faceB }; // Retrieve distances from each endpoint to the line float distanceA = MathVector2DotProduct(normal, *faceA) - clip; float distanceB = MathVector2DotProduct(normal, *faceB) - clip; // If negative (behind plane) if (distanceA <= 0.0f) out[sp++] = *faceA; if (distanceB <= 0.0f) out[sp++] = *faceB; // If the points are on different sides of the plane if ((distanceA*distanceB) < 0.0f) { // Push intersection point float alpha = distanceA/(distanceA - distanceB); out[sp] = *faceA; Vector2 delta = MathVector2Subtract(*faceB, *faceA); delta.x *= alpha; delta.y *= alpha; out[sp] = MathVector2Add(out[sp], delta); sp++; } // Assign the new converted values *faceA = out[0]; *faceB = out[1]; return sp; } // Returns the barycenter of a triangle given by 3 points static Vector2 MathTriangleBarycenter(Vector2 v1, Vector2 v2, Vector2 v3) { Vector2 result = { 0.0f, 0.0f }; result.x = (v1.x + v2.x + v3.x)/3; result.y = (v1.y + v2.y + v3.y)/3; return result; } // Returns the cross product of a vector and a value static inline Vector2 MathVector2Product(Vector2 vector, float value) { Vector2 result = { -value*vector.y, value*vector.x }; return result; } // Returns the cross product of two vectors static inline float MathVector2CrossProduct(Vector2 v1, Vector2 v2) { return (v1.x*v2.y - v1.y*v2.x); } // Returns the len square root of a vector static inline float MathVector2SqrLen(Vector2 vector) { return (vector.x*vector.x + vector.y*vector.y); } // Returns the dot product of two vectors static inline float MathVector2DotProduct(Vector2 v1, Vector2 v2) { return (v1.x*v2.x + v1.y*v2.y); } // Returns the square root of distance between two vectors static inline float MathVector2SqrDistance(Vector2 v1, Vector2 v2) { Vector2 dir = MathVector2Subtract(v1, v2); return MathVector2DotProduct(dir, dir); } // Returns the normalized values of a vector static void MathVector2Normalize(Vector2 *vector) { float length, ilength; Vector2 aux = *vector; length = sqrtf(aux.x*aux.x + aux.y*aux.y); if (length == 0) length = 1.0f; ilength = 1.0f/length; vector->x *= ilength; vector->y *= ilength; } // Returns the sum of two given vectors static inline Vector2 MathVector2Add(Vector2 v1, Vector2 v2) { Vector2 result = { v1.x + v2.x, v1.y + v2.y }; return result; } // Returns the subtract of two given vectors static inline Vector2 MathVector2Subtract(Vector2 v1, Vector2 v2) { Vector2 result = { v1.x - v2.x, v1.y - v2.y }; return result; } // Creates a matrix 2x2 from a given radians value static Matrix2x2 MathMatFromRadians(float radians) { float cos = cosf(radians); float sin = sinf(radians); Matrix2x2 result = { cos, -sin, sin, cos }; return result; } // Returns the transpose of a given matrix 2x2 static inline Matrix2x2 MathMatTranspose(Matrix2x2 matrix) { Matrix2x2 result = { matrix.m00, matrix.m10, matrix.m01, matrix.m11 }; return result; } // Multiplies a vector by a matrix 2x2 static inline Vector2 MathMatVector2Product(Matrix2x2 matrix, Vector2 vector) { Vector2 result = { matrix.m00*vector.x + matrix.m01*vector.y, matrix.m10*vector.x + matrix.m11*vector.y }; return result; } #endif // PHYSAC_IMPLEMENTATION