/// <summary>
/// Given a point, a distance for the project, and an angle, find (x3, x4) from the projection.
/// </summary>
/// <param name="x1"></param>
/// <param name="x2"></param>
/// <param name="distance"></param>
/// <param name="angle"></param>
/// <returns></returns>
public static DoublePoint findProjection(double x1, double x2, double distance, double angle)
{
DoublePoint ret = new DoublePoint();
// Special case if the angle is 0
if (angle == 0)
{
ret.x1 = x1 + distance;
ret.x2 = x2;
return ret;
} // or 180
else if (angle == 180)
{
ret.x1 = x1 - distance;
ret.x2 = x2;
return ret;
} // or 90
else if (angle == 90)
{
ret.x1 = x1;
ret.x2 = x2 + distance;
return ret;
} // or 270
else if (angle == 270)
{
ret.x1 = x1;
ret.x2 = x2 - distance;
return ret;
}
// IF none of those, calculate x3 and x4
double x3 = Math.Abs(Math.Cos(angle * Math.PI / 180d) * distance);
double x4 = Math.Abs(Math.Sin(angle * Math.PI / 180d) * distance);
// If the angle was in quadrant 1, add x1 and x3, add x2 and x4
if (angle > 0 && angle < 90)
{
ret.x1 = x1 + x3;
ret.x2 = x2 + x4;
}
// If the angle was in quadrant 2, subtract x3 from x1, add x2 and x4
else if (angle > 90 && angle < 180)
{
ret.x1 = x1 - x3;
ret.x2 = x2 + x4;
} // If the angle was in quadrant 3, subtract x3 from x1, subtract x4 from x2
else if (angle > 180 && angle < 270)
{
ret.x1 = x1 - x3;
ret.x2 = x2 - x4;
} // If the angle was in quadrant 4, add x1 and x3, subtract x4 from x2
else
{
ret.x1 = x1 + x3;
ret.x2 = x2 - x4;
}
return ret;
}
/// <summary>
/// Returns an intersection between the first two point-lines and the second two point-lines.
/// </summary>
/// <param name="x1">Line 1</param>
/// <param name="y1">Line 1</param>
/// <param name="x2">Line 1</param>
/// <param name="y2">Line 1</param>
/// <param name="x3">Line 2</param>
/// <param name="y3">Line 2</param>
/// <param name="x4">Line 2</param>
/// <param name="y4">Line 2</param>
/// <returns></returns>
public static DoublePoint getValidIntersect(double x1, double y1, double x2, double y2, double x3, double y3, double x4, double y4)
{
DoublePoint intersect = new DoublePoint();
double distAB, theCos, theSin, newX, ABpos ;
// Fail if either line segment is zero-length.
if (x1==x2 && y1==y2 || x3==x4 && y3==y4)
return null;
// Fail if the segments share an end-point.
if (x1==x3 && y1==y3 || x2==x3 && y2==y3
|| x1==x4 && y1==y4 || x2==x4 && y2==y4)
return null;
// (1) Translate the system so that point A is on the origin.
x2-=x1; y2-=y1;
x3-=x1; y3-=y1;
x4-=x1; y4-=y1;
// Discover the length of segment A-B.
distAB=Math.Sqrt(x2*x2+y2*y2);
// (2) Rotate the system so that point B is on the positive X axis.
theCos=x2/distAB;
theSin=y2/distAB;
newX=x3*theCos+y3*theSin;
y3 =y3*theCos-x3*theSin; x3=newX;
newX=x4*theCos+y4*theSin;
y4 =y4*theCos-x4*theSin; x4=newX;
// Fail if segment C-D doesn't cross line A-B.
if (y3<0 && y4<0 || y3>=0 && y4>=0)
return null;
// (3) Discover the position of the intersection point along line A-B.
ABpos=x4+(x3-x4)*y4/(y4-y3);
// Fail if segment C-D crosses line A-B outside of segment A-B.
if (ABpos<0 || ABpos>distAB) return null;
// (4) Apply the discovered position to line A-B in the original coordinate system.
intersect.x1 = x1 + ABpos * theCos;
intersect.x2 = y1 + ABpos * theSin;
// Success.
return intersect;
}
/// <summary>
/// Determines whether it is valid intersect with the specified wall vertices.
/// </summary>
/// <param name="wallVertices">The wall vertices</param>
/// <param name="intersect">The intersect</param>
/// <param name="iWallCollided">The index of the wall collided</param>
/// <returns>
/// <c>true</c> if it is valid intersect with the specified wall vertices. Otherwise, <c>false</c>.
/// </returns>
public static bool isValidIntersect(List<DoublePoint> wallVertices, Intersect intersect, int iWallCollided = 0)
{
int tempMod = (int)MathUtilities.mod(iWallCollided - 1, wallVertices.Count); // Use tempMod to find the correct vertex to determine a line for the current wall
// Run through the current walls' vertices and determine the min and max for the x position and min and max for the y position
DoublePoint minXPoint = new DoublePoint();
DoublePoint maxXPoint = new DoublePoint();
DoublePoint minYPoint = new DoublePoint();
DoublePoint maxYPoint = new DoublePoint();
if (wallVertices[tempMod].x1 > wallVertices[iWallCollided].x1)
{
minXPoint.x1 = wallVertices[iWallCollided].x1;
minXPoint.x2 = wallVertices[iWallCollided].x2;
maxXPoint.x1 = wallVertices[tempMod].x1;
maxXPoint.x2 = wallVertices[tempMod].x2;
}
else
{
minXPoint.x1 = wallVertices[tempMod].x1;
minXPoint.x2 = wallVertices[tempMod].x2;
maxXPoint.x1 = wallVertices[iWallCollided].x1;
maxXPoint.x2 = wallVertices[iWallCollided].x2;
}
if (wallVertices[tempMod].x2 > wallVertices[iWallCollided].x2)
{
minYPoint.x1 = wallVertices[iWallCollided].x1;
minYPoint.x2 = wallVertices[iWallCollided].x2;
maxYPoint.x1 = wallVertices[tempMod].x1;
maxYPoint.x2 = wallVertices[tempMod].x2;
}
else
{
minYPoint.x1 = wallVertices[tempMod].x1;
minYPoint.x2 = wallVertices[tempMod].x2;
maxYPoint.x1 = wallVertices[iWallCollided].x1;
maxYPoint.x2 = wallVertices[iWallCollided].x2;
}
// Use this data to determine whether the collision we found is actually a valid collision (inside the shape)
return (intersect.x1 >= minXPoint.x1 && intersect.x1 <= maxXPoint.x1 &&
intersect.x2 >= minYPoint.x2 && intersect.x2 <= maxYPoint.x2);
}
/// <summary>
/// Gets the intersection between the lines (x1, y1), (x2, y1) and (x3, y3), (x4, y4)
/// </summary>
/// <param name="x1">Line 1</param>
/// <param name="y1">Line 1</param>
/// <param name="x2">Line 1</param>
/// <param name="y2">Line 1</param>
/// <param name="x3">Line 2</param>
/// <param name="y3">Line 2</param>
/// <param name="x4">Line 2</param>
/// <param name="y4">Line 2</param>
/// <returns></returns>
public static DoublePoint getIntersect(double x1, double y1, double x2, double y2, double x3, double y3, double x4, double y4)
{
DoublePoint ret = new DoublePoint();
// Special case for when the first line is vertical
if (x2 - x1 == 0)
{
double m2 = (y4 - y3) / (x4 - x3);
double b2 = y3 - (m2 * x3);
ret.x1 = x1;
ret.x2 = (m2 * x1) + b2;
return ret;
}
// Special case for when the first line is vertical
else if (x4 - x3 == 0)
{
double m1 = (y2 - y1) / (x2 - x1);
double b1 = y1 - (m1 * x1);
ret.x1 = x3;
ret.x2 = m1 * x3 + b1;
return ret;
}
else
{
double m1 = (y2 - y1) / (x2 - x1); // If not those two, get the slope of both lines
double m2 = (y4 - y3) / (x4 - x3);
if (m1 != m2) // If they're not parallel
{
double b1 = y1 - (m1 * x1); // Get their y-intercepts
double b2 = y3 - (m2 * x3); // Get their y-intercepts
ret.x1 = (b2 - b1) / (m1 - m2); // Solve for x of the interception
ret.x2 = m2 * ret.x1 + b2; // Solve for y of the interception
return ret;
}
return null;
}
}