/*
This function reflects an animated circle on a static circle.
It should first make sure that the animated circle is intersecting with the static one
- Parameters
- Center0s: The starting position of the animated circle's center
- Center0e: The ending position of the animated circle's center
- Radius0: The animated circle's radius
- Center1: The static circle's center
- Radius1: The static circle's radius
- Pi: This will be used to store the intersection point's coordinates (In case there's an intersection)
- R: Reflected vector R
- Returned value: Intersection time t
- -1.0f: If there's no intersection
- Intersection time: If there's an intersection
*/
float ReflectAnimatedCircleOnStaticCircle(Vector2D *Center0s, Vector2D *Center0e, float Radius0, Vector2D *Center1, float Radius1, Vector2D *Pi, Vector2D *R)
{
Vector2D U; //(U is the adjusted normal)
Vector2D M; //(M is from Ps to Pi)
Vector2D Normal;
float UScalar;
float IntersectionTime = AnimatedCircleToStaticCircle(Center0s, Center0e, Radius0, Center1, Radius1, Pi);
if (IntersectionTime == -1.0f)
return -1.0f;
// Calculating Normal
Vector2DSub(&Normal, Pi, Center1);
Vector2DNormalize(&Normal, &Normal);
// Calculating Vector M (M is from Ps to Pi)
Vector2DSub(&M, Center0s, Pi);
//Calculating Vector U (U is the adjusted normal)
UScalar = Vector2DDotProduct(&M, &Normal);
Vector2DScale(&U, &Normal, UScalar);
//Calculating R (R is the reflection Vector)
Vector2DScale(&U, &U, 2.0f);
Vector2DSub(R, &U, &M);
Vector2DNormalize(R, R);
return IntersectionTime;
}
/*
This function checks whether an animated circle is colliding with a line segment
- Parameters
- Ps: The center's starting location
- Pe: The center's ending location
- Radius: The circle's radius
- LS: The line segment
- Pi: This will be used to store the intersection point's coordinates (In case there's an intersection)
- Returned value: Intersection time t
- -1.0f: If there's no intersection
- Intersection time: If there's an intersection
*/
float AnimatedCircleToStaticLineSegment(Vector2D *Ps, Vector2D *Pe, float Radius, LineSegment2D *LS, Vector2D *Pi)
{
Vector2D Vector;
Vector2D P1Vector;
Vector2D P0Vector;
float InsideorOutside;
float P1P0Dot;
float IntersectionTime;
float temp1;
float temp2;
if (StaticPointToStaticLineSegment(Ps, LS) < -Radius && StaticPointToStaticLineSegment(Pe, LS) < -Radius)
{
return NO_INTERSECTION;
}
else if (StaticPointToStaticLineSegment(Ps, LS) > Radius && StaticPointToStaticLineSegment(Pe, LS) > Radius)
{
return NO_INTERSECTION;
}
InsideorOutside = StaticPointToStaticLineSegment(Ps, LS);
temp1 = Vector2DDotProduct(&LS->mN, Ps);
temp1 = LS->mNdotP0 - temp1;
if (InsideorOutside > 0)
temp1 += Radius;
else if (InsideorOutside < 0)
temp1 -= Radius;
Vector2DSub(&Vector, Pe, Ps);
temp2 = Vector2DDotProduct(&LS->mN, &Vector);
IntersectionTime = temp1 / temp2;
if (IntersectionTime >= 0 && IntersectionTime <= 1)
{
Vector2DScale(&Vector, &Vector, IntersectionTime);
Vector2DAdd(Pi, Ps, &Vector);
Vector2DSub(&P1Vector, Pi, &LS->mP1);
Vector2DSub(&P0Vector, Pi, &LS->mP0);
P1P0Dot = Vector2DDotProduct(&P0Vector, &P1Vector);
if (P1P0Dot < 0)
{
return IntersectionTime;
}
else
{
return NO_INTERSECTION;
}
}
return NO_INTERSECTION;
}
/*
This function reflects an animated circle on a line segment.
It should first make sure that the animated point is intersecting with the line
- Parameters
- Ps: The center's starting location
- Pe: The center's ending location
- Radius: The circle's radius
- LS: The line segment
- Pi: This will be used to store the intersection point's coordinates (In case there's an intersection)
- R: Reflected vector R
- Returned value: Intersection time t
- -1.0f: If there's no intersection
- Intersection time: If there's an intersection
*/
float ReflectAnimatedCircleOnStaticLineSegment(Vector2D *Ps, Vector2D *Pe, float Radius, LineSegment2D *LS, Vector2D *Pi, Vector2D *R)
{
float IntersectionTime = AnimatedCircleToStaticLineSegment(Ps, Pe, Radius, LS, Pi);
float Scalar;
Vector2D I;
Vector2D S;
Vector2D Vector;
if (IntersectionTime == NO_INTERSECTION)
{
return NO_INTERSECTION;
}
Vector2DSub(&I, Pe, Pi); // Creates the I vector
Scalar = Vector2DDotProduct(&I, &LS->mN); // Creates the scalar needed for the s vector
Vector2DScale(&S, &LS->mN, Scalar); // Creates the S vector
Vector2DSub(R, &I, &S);
Vector2DSub(R, R, &S);
return IntersectionTime;
}
/*
This function checks whether an animated point is colliding with a static circle
- Parameters
- Ps: The point's starting location
- Pe: The point's ending location
- Center: The circle's center
- Radius: The circle's radius
- Pi: This will be used to store the intersection point's coordinates (In case there's an intersection)
- Returned value: Intersection time t
- -1.0f: If there's no intersection
- Intersection time: If there's an intersection
*/
float AnimatedPointToStaticCircle(Vector2D *Ps, Vector2D *Pe, Vector2D *Center, float Radius, Vector2D *Pi)
{
float A = 0;
float B = 0;
float C = 0;
float Deter = 0;
float IntersectionTime = 0;
float Ti0 = 0;
float Ti1 = 0;
Vector2D PstoCenter;
Vector2D Vector;
Vector2D Temp;
Vector2DSub(&Vector, Pe, Ps);
Vector2DSub(&PstoCenter, Center, Ps);
Vector2DSub(&Temp, Center, Ps);
// A Solved Here!
A = Vector2DDotProduct(&Vector, &Vector);
// B Solved Here!
Vector2DScale(&Temp, &PstoCenter, -2.0f);
B = Vector2DDotProduct(&Temp, &Vector);
// C Solved Here!
C = Vector2DDotProduct(&PstoCenter, &PstoCenter);
C -= (Radius * Radius);
// Solving for (B^2 - 4AC)
Deter += (B * B);
Deter -= (4 * A * C);
if (Deter < 0)
return -1.0f;
else if (Deter == 0)
IntersectionTime = (-B / (2 * A));
else if (Deter > 0)
{
Ti0 = (-B - sqrt(Deter)) / (2 * A);
Ti1 = (-B + sqrt(Deter)) / (2 * A);
if (Ti0 > Ti1)
IntersectionTime = Ti1;
else
IntersectionTime = Ti0;
}
Vector2DScaleAdd(Pi, &Vector, Ps, IntersectionTime);
return IntersectionTime;
}
/*
This function checks whether an animated point is colliding with a line segment
- Parameters
- Ps: The point's starting location
- Pe: The point's ending location
- LS: The line segment
- Pi: This will be used to store the intersection point's coordinates (In case there's an intersection)
- Returned value: Intersection time t
- -1.0f: If there's no intersection
- Intersection time: If there's an intersection
*/
float AnimatedPointToStaticLineSegment(Vector2D *Ps, Vector2D *Pe, LineSegment2D *LS, Vector2D *Pi)
{
Vector2D Vector;
Vector2D P1Vector;
Vector2D P0Vector;
float P1P0Dot;
float IntersectionTime;
float temp1;
float temp2;
temp1 = Vector2DDotProduct(&LS->mN, Ps);
temp1 = LS->mNdotP0 - temp1;
Vector2DSet(&Vector, Pe->x - Ps->x, Pe->y - Ps->y);
temp2 = Vector2DDotProduct(&LS->mN, &Vector);
IntersectionTime = temp1 / temp2;
if (IntersectionTime >= 0 && IntersectionTime <= 1)
{
Vector2DScale(&Vector, &Vector, IntersectionTime);
Vector2DAdd(Pi, Ps, &Vector);
Vector2DSet(&P1Vector, Pi->x - LS->mP1.x, Pi->y - LS->mP1.y);
Vector2DSet(&P0Vector, Pi->x - LS->mP0.x, Pi->y - LS->mP0.y);
P1P0Dot = Vector2DDotProduct(&P0Vector, &P1Vector);
if (P1P0Dot < 0)
{
return IntersectionTime;
}
else
{
return NO_INTERSECTION;
}
}
else
{
return NO_INTERSECTION;
}
}
/*
This function checks whether an animated circle is colliding with a static circle
- Parameters
- Center0s: The starting position of the animated circle's center
- Center0e: The ending position of the animated circle's center
- Radius0: The animated circle's radius
- Center1: The static circle's center
- Radius1: The static circle's radius
- Pi: This will be used to store the intersection point's coordinates (In case there's an intersection)
- Returned value: Intersection time t
- -1.0f: If there's no intersection
- Intersection time: If there's an intersection
*/
float AnimatedCircleToStaticCircle(Vector2D *Center0s, Vector2D *Center0e, float Radius0, Vector2D *Center1, float Radius1, Vector2D *Pi)
{
float A = 0;
float B = 0;
float C = 0;
float Deter = 0;
float IntersectionTime = 0;
float Ti0 = 0;
float Ti1 = 0;
float M;
Vector2D PstoCenter;
Vector2D Vector;
Vector2D Temp;
Vector2DSub(&Vector, Center0e, Center0s);
Vector2DSub(&PstoCenter, Center1, Center0s);
Vector2DSub(&Temp, Center1, Center0s);
M = Vector2DDotProduct(&PstoCenter, &Vector);
if (M < 0)
return -1.0f;
// A Solved Here!
A = Vector2DDotProduct(&Vector, &Vector);
// B Solved Here!
Vector2DScale(&Temp, &PstoCenter, -2.0f);
B = Vector2DDotProduct(&Temp, &Vector);
// C Solved Here!
C = Vector2DDotProduct(&PstoCenter, &PstoCenter);
C -= (Radius1 + Radius0) * (Radius1 + Radius0);
// Solving for (B^2 - 4AC)
Deter += (B * B);
Deter -= (4 * A * C);
if (Deter < 0)
return -1.0f;
else if (Deter == 0)
IntersectionTime = (-B / (2 * A));
else if (Deter > 0)
{
Ti0 = (-B - sqrt(Deter)) / (2 * A);
Ti1 = (-B + sqrt(Deter)) / (2 * A);
if (Ti0 > Ti1)
IntersectionTime = Ti1;
else
IntersectionTime = Ti0;
}
if (IntersectionTime > 0 && IntersectionTime < 1)
{
Vector2DScaleAdd(Pi, &Vector, Center0s, IntersectionTime);
return IntersectionTime;
}
return -1.0f;
}
int main()
{
Vector2D v1, v2, v3, result;
float scale;
Matrix2D id, m0, m1;
Vector2D u;
float d, x, y;
long n;
long i, j;
float radius;
v1.x = v1.y = 7.0f;
Vector2DZero(&v1);
result.x = result.y = 0.0f;
printf("Vector2DZero: %s\n", (CompareVector2D(&result, &v1) < EPSILON) ? "Pass" : "Fail");
Vector2DSet(&v1, 1.0f, 2.0f);
result.x = 1.0f; result.y = 2.0f;
printf("Vector2DSet: %s\n", (CompareVector2D(&result, &v1) < EPSILON) ? "Pass" : "Fail");
v1.x = 2.0f; v1.y = -4.0f;
Vector2DNeg(&v2, &v1);
result.x = -2.0f; result.y = 4.0f;
printf("Vector2DNeg: %s\n", (CompareVector2D(&result, &v2) < EPSILON) ? "Pass" : "Fail");
v1.x = 2.0f; v1.y = -4.0f;
v2.x = 1.0f; v2.y = 7.0f;
Vector2DAdd(&v3, &v1, &v2);
result.x = result.y = 3.0f;
printf("Vector2DAdd: %s\n", (CompareVector2D(&result, &v3) < EPSILON) ? "Pass" : "Fail");
v1.x = 2.0f; v1.y = -4.0f;
v2.x = 1.0f; v2.y = 7.0f;
Vector2DSub(&v3, &v1, &v2);
result.x = 1.0f; result.y = -11.0f;
printf("Vector2DSub: %s\n", (CompareVector2D(&result, &v3) < EPSILON) ? "Pass" : "Fail");
v1.x = 3.0f; v1.y = 4.0f;
Vector2DNormalize(&v2, &v1);
result.x = 0.6f; result.y = 0.8f;
printf("Vector2DNormalize: %s\n", (CompareVector2D(&result, &v2) < EPSILON) ? "Pass" : "Fail");
v1.x = 2.0f; v1.y = -5.0f;
Vector2DScale(&v2, &v1, 3.0f);
result.x = 6.0f; result.y = -15.0f;
printf("Vector2DScale: %s\n", (CompareVector2D(&result, &v2) < EPSILON) ? "Pass" : "Fail");
v1.x = 2.0f; v1.y = -5.0f;
v2.x = 6.0f; v2.y = 2.0f;
scale = 3.0f;
Vector2DScaleAdd(&v3, &v1, &v2, scale);
result.x = 12.0f; result.y = -13.0f;
printf("Vector2DScaleAdd: %s\n", (CompareVector2D(&result, &v3) < EPSILON) ? "Pass" : "Fail");
Vector2DScaleSub(&v3, &v1, &v2, scale);
result.x = 0.f; result.y = -17.f;
printf("Vector2DScaleSub: %s\n", (CompareVector2D(&result, &v3) < EPSILON) ? "Pass" : "Fail");
v1.x = 3.0f; v1.y = -4.0f;
printf("Vector2DLength: %s\n", (fabs(Vector2DLength(&v1) - 5.0f) < EPSILON) ? "Pass" : "Fail");
v1.x = 3.0f; v1.y = -4.0f;
printf("Vector2DSquareLength: %s\n", (fabs(Vector2DSquareLength(&v1) - 25.0f) < EPSILON) ? "Pass" : "Fail");
v1.x = 2.0f; v1.y = 3.0f;
v2.x = 4.0f; v2.y = -1.0f;
printf("Vector2DDistance: %s\n", (fabs(Vector2DDistance(&v1, &v2) - 4.472136) < EPSILON) ? "Pass" : "Fail");
v1.x = 2.0f; v1.y = 3.0f;
v2.x = 4.0f; v2.y = -1.0f;
printf("Vector2DSquareDistance: %s\n", (fabs(Vector2DSquareDistance(&v1, &v2) - 20.0f) < EPSILON) ? "Pass" : "Fail");
v1.x = 3.0f; v1.y = 2.0f;
v2.x = 4.0f; v2.y = -6.0f;
printf("Vector2DDotProduct: %s\n", (fabs(Vector2DDotProduct(&v1, &v2)) < EPSILON) ? "Pass" : "Fail");
printf("\n------Testing StaticPointToStaticCircle------\n\n");
v1.x = 10.f; v1.y = 10.f;
v2.x = 11.4f; v2.y = 11.4f;
radius = 2.f;
printf("StaticPointToStaticCircle Collision: %s\n", (StaticPointToStaticCircle(&v2, &v1, radius)) ? "Pass" : "Fail" );
v2.x = 12.f; v2.y = 12.f;
printf("StaticPointToStaticCircle Non Collision: %s\n", (!StaticPointToStaticCircle(&v2, &v1, radius)) ? "Pass" : "Fail" );
printf("\n------Running Matrix Tests------\n\n");
// create an id matrix for reference
for (i = 0; i < 3; i++)
for (j = 0; j < 3; j++)
id.m[j][i] = (i == j) ? 1.0f : 0.0f;
// ====================
// test Matrix2DIdentity
// ====================
Matrix2DIdentity(&m0);
d = CompareMatrix2D(&id, &m0);
printf("Matrix2DIdentity : %s\n", (CompareMatrix2D(&id, &m0) < EPSILON) ? "Pass" : "Fail");
// ====================
// test Matrix2DTrans
// ====================
// generate 2 random numbers
x = 2.0f * rand() / (float)(RAND_MAX) - 1.0f;
y = 2.0f * rand() / (float)(RAND_MAX) - 1.0f;
Matrix2DTranslate(&m0, x, y);
m0.m[0][2] -= x;
m0.m[1][2] -= y;
printf("Matrix2DTranslate: %s\n", (CompareMatrix2D(&id, &m0) < EPSILON) ? "Pass" : "Fail");
// ====================
// test Matrix2DScale
// ====================
// generate 2 random numbers
x = 2.0f * rand() / (float)(RAND_MAX) - 1.0f;
y = 2.0f * rand() / (float)(RAND_MAX) - 1.0f;
Matrix2DScale(&m0, x, y);
m0.m[0][0] /= x;
m0.m[1][1] /= y;
printf("Matrix2DScale : %s\n", (CompareMatrix2D(&id, &m0) < EPSILON) ? "Pass" : "Fail");
// ====================
// test Matrix2DConcat
// ====================
// generate 2 random numbers
x = 2.0f * rand() / (float)(RAND_MAX) - 1.0f;
y = 2.0f * rand() / (float)(RAND_MAX) - 1.0f;
Matrix2DTranslate (&m0, x, y);
Matrix2DScale (&m1, x, y);
Matrix2DConcat(&m0, &m0, &m1);
m0.m[0][2] -= x;
m0.m[1][2] -= y;
m0.m[0][0] /= x;
m0.m[1][1] /= y;
printf("Matrix2DConcat 1 : %s\n", (CompareMatrix2D(&id, &m0) < EPSILON) ? "Pass" : "Fail");
// generate 2 random numbers
x = 2.0f * rand() / (float)(RAND_MAX) - 1.0f;
y = 2.0f * rand() / (float)(RAND_MAX) - 1.0f;
Matrix2DTranslate (&m0, x, y);
Matrix2DScale (&m1, x, y);
Matrix2DConcat(&m0, &m1, &m0);
m0.m[0][2] -= x * x;
m0.m[1][2] -= y * y;
m0.m[0][0] /= x;
m0.m[1][1] /= y;
printf("Matrix2DConcat 2 : %s\n", (CompareMatrix2D(&id, &m0) < EPSILON) ? "Pass" : "Fail");
// ====================
// test Matrix2DRotRad
// ====================
n = (rand() % 16) + 15;
Matrix2DIdentity(&m0);
Matrix2DRotRad (&m1, 2.0f * PI / n);
for (i = 0; i < n; i++)
Matrix2DConcat(&m0, &m1, &m0);
printf("Matrix2DRotRad : %s (%d)\n", (CompareMatrix2D(&id, &m0) < EPSILON) ? "Pass" : "Fail", n);
// ====================
// test Matrix2DRotDeg
// ====================
n = (rand() % 16) + 15;
Matrix2DIdentity(&m0);
Matrix2DRotDeg (&m1, 360.0f / n);
for (i = 0; i < n; i++)
Matrix2DConcat(&m0, &m1, &m0);
printf("Matrix2DRotDeg : %s (%d)\n", (CompareMatrix2D(&id, &m0) < EPSILON) ? "Pass" : "Fail", n);
// ====================
// test Matrix2DTranspose
// ====================
Matrix2DRotRad (&m0, rand() / (float)(RAND_MAX) * 2.0f * PI);
Matrix2DTranspose(&m1, &m0);
Matrix2DConcat (&m0, &m1, &m0);
printf("Matrix2DTranspose: %s\n", (CompareMatrix2D(&id, &m0) < EPSILON) ? "Pass" : "Fail");
// ====================
// test Matrix2DMultVec
// ====================
// generate 2 random numbers
x = 2.0f * rand() / (float)(RAND_MAX) - 1.0f;
y = 2.0f * rand() / (float)(RAND_MAX) - 1.0f;
n = (rand() % 16) + 15;
Vector2DSet (&u, x, y);
Matrix2DRotRad (&m0, 2.0f * PI / n);
for (i = 0; i < n; i++)
Matrix2DMultVec(&u, &m0, &u);
printf("Matrix2DMultVec : %s\n", ((fabs(u.x - x) + fabs(u.y - y)) < EPSILON) ? "Pass" : "Fail");
// generate 2 random numbers
x = 2.0f * rand() / (float)(RAND_MAX) - 1.0f;
y = 2.0f * rand() / (float)(RAND_MAX) - 1.0f;
n = (rand() % 16) + 15;
Vector2DSet (&u, x, y);
Matrix2DTranslate (&m0, x, y);
for (i = 1; i < n; i++)
Matrix2DMultVec(&u, &m0, &u);
printf("Matrix2DMultVec : %s\n", ((fabs(u.x - x * n) + fabs(u.y - y * n)) < EPSILON) ? "Pass" : "Fail");
printf("\n------Testing New Collision Functions------\n\n");
//StaticPointToStaticRect
Vector2DSet(&v1, 1.f, 1.f); //point
Vector2DSet(&v2, 0.f, 0.f); //rect
printf("StaticPointToStaticRect Collision: %s\n", (StaticPointToStaticRect(&v1, &v2, 2.f, 2.f) ? "Pass" : "Fail"));
printf("StaticPointToStaticRect Non Collision: %s\n\n", (!StaticPointToStaticRect(&v1, &v2, 1.f, 1.f) ? "Pass" : "Fail"));
//StaticCircleToStaticCircle
Vector2DSet(&v1, 2.f, 0.f);
printf("StaticCircleToStaticCircle Collision Touch: %s\n", (StaticCircleToStaticCircle(&v1, 1.f, &v2, 1.f) ? "Pass" : "Fail"));
printf("StaticCircleToStaticCircle Collision: %s\n", (StaticCircleToStaticCircle(&v1, 2.f, &v2, 1.f) ? "Pass" : "Fail"));
printf("StaticCircleToStaticCircle Non Collision: %s\n\n", (!StaticCircleToStaticCircle(&v1, 0.5f, &v2, 1.f) ? "Pass" : "Fail"));
//StaticRectToStaticRect
Vector2DSet(&v1, 2.f, 2.f);
printf("StaticRectToStaticRect Non Collision: %s\n", (!StaticRectToStaticRect(&v1, 1.f, 1.f, &v2, 1.f, 1.f) ? "Pass" : "Fail"));
printf("StaticRectToStaticRect Collision Touch: %s\n", (StaticRectToStaticRect(&v1, 2.f, 2.f, &v2, 2.f, 2.f) ? "Pass" : "Fail"));
printf("StaticRectToStaticRect Collision Intersect: %s\n", (StaticRectToStaticRect(&v1, 3.f, 3.f, &v2, 3.f, 3.f) ? "Pass" : "Fail"));
return 1;
}
void Vector2DScaleSub(Vector2D &Result, const Vector2D &Vec0, const Vector2D &Vec1, float c)
{
Vector2DScale(Result, Vec0, c);
Vector2DSub(Result, Result, Vec1);
}
void Vector2DScaleAdd(Vector2D &Result, const Vector2D &Vec0, const Vector2D &Vec1, float c)
{
Vector2D tempScale;
Vector2DScale(tempScale, Vec0, c);
Vector2DAdd(Result, tempScale, Vec1);
}
void Vector2DScaleSub(Vector2D *pResult, Vector2D *pVec0, Vector2D *pVec1, float c) {
Vector2DScale(pResult, pVec0, c);
Vector2DSub(pResult, pResult, pVec1);
}
void Vector2DScaleAdd(Vector2D *pResult, Vector2D *pVec0, Vector2D *pVec1, float c) {
Vector2DScale(pResult, pVec0, c);
Vector2DAdd(pResult, pResult, pVec1);
}
void Vector2DNormalize(Vector2D *pResult, Vector2D *pVec0) {
Vector2DScale(pResult, pVec0, (1 / Vector2DLength(pVec0)));
}