#include "pch.h" #include <algorithm> #include <iostream> #include <cmath> #include "utils.h" unsigned int utils::GetIdx(int x, int y, int cols) { return (x + cols * y); } #pragma region OpenGLDrawFunctionality void utils::SetColor( const Color4f& color ) { glColor4f( color.r, color.g, color.b, color.a ); } void utils::DrawPoint( float x, float y, float pointSize ) { glPointSize( pointSize ); glBegin( GL_POINTS ); { glVertex2f( x, y ); } glEnd( ); } void utils::DrawPoint( const Point2f& p, float pointSize ) { DrawPoint( p.x, p.y, pointSize ); } void utils::DrawPoints( Point2f *pVertices, int nrVertices, float pointSize ) { glPointSize( pointSize ); glBegin( GL_POINTS ); { for ( int idx{ 0 }; idx < nrVertices; ++idx ) { glVertex2f( pVertices[idx].x, pVertices[idx].y ); } } glEnd( ); } void utils::DrawLine( float x1, float y1, float x2, float y2, float lineWidth ) { glLineWidth( lineWidth ); glBegin( GL_LINES ); { glVertex2f( x1, y1 ); glVertex2f( x2, y2 ); } glEnd( ); } void utils::DrawLine( const Point2f& p1, const Point2f& p2, float lineWidth ) { DrawLine( p1.x, p1.y, p2.x, p2.y, lineWidth ); } void utils::DrawRect( float left, float bottom, float width, float height, float lineWidth ) { glLineWidth( lineWidth ); glBegin( GL_LINE_LOOP ); { glVertex2f( left, bottom ); glVertex2f( left + width, bottom ); glVertex2f( left + width, bottom + height ); glVertex2f( left, bottom + height ); } glEnd( ); } void utils::DrawRect( const Point2f& bottomLeft, float width, float height, float lineWidth ) { DrawRect( bottomLeft.x, bottomLeft.y, width, height, lineWidth ); } void utils::DrawRect( const Rectf& rect, float lineWidth ) { DrawRect( rect.left, rect.bottom, rect.width, rect.height, lineWidth ); } void utils::FillRect( float left, float bottom, float width, float height ) { glBegin( GL_POLYGON ); { glVertex2f( left, bottom ); glVertex2f( left + width, bottom ); glVertex2f( left + width, bottom + height ); glVertex2f( left, bottom + height ); } glEnd( ); } void utils::FillRect( const Point2f& bottomLeft, float width, float height ) { FillRect( bottomLeft.x, bottomLeft.y, width, height ); } void utils::FillRect( const Rectf& rect ) { FillRect( rect.left, rect.bottom, rect.width, rect.height ); } void utils::DrawEllipse( float centerX, float centerY, float radX, float radY, float lineWidth ) { float dAngle{ radX > radY ? float( g_Pi / radX ) : float( g_Pi / radY ) }; glLineWidth( lineWidth ); glBegin( GL_LINE_LOOP ); { for ( float angle = 0.0; angle < float( 2 * g_Pi ); angle += dAngle ) { glVertex2f( centerX + radX * float( cos( angle ) ), centerY + radY * float( sin( angle ) ) ); } } glEnd( ); } void utils::DrawEllipse( const Point2f& center, float radX, float radY, float lineWidth ) { DrawEllipse( center.x, center.y, radX, radY, lineWidth ); } void utils::DrawEllipse( const Ellipsef& ellipse, float lineWidth ) { DrawEllipse( ellipse.center.x, ellipse.center.y, ellipse.radiusX, ellipse.radiusY, lineWidth ); } void utils::FillEllipse( float centerX, float centerY, float radX, float radY ) { float dAngle{ radX > radY ? float( g_Pi / radX ) : float( g_Pi / radY ) }; glBegin( GL_POLYGON ); { for ( float angle = 0.0; angle < float( 2 * g_Pi ); angle += dAngle ) { glVertex2f( centerX + radX * float( cos( angle ) ), centerY + radY * float( sin( angle ) ) ); } } glEnd( ); } void utils::FillEllipse( const Ellipsef& ellipse ) { FillEllipse( ellipse.center.x, ellipse.center.y, ellipse.radiusX, ellipse.radiusY ); } void utils::FillEllipse( const Point2f& center, float radX, float radY ) { FillEllipse( center.x, center.y, radX, radY ); } void utils::DrawArc( float centerX, float centerY, float radX, float radY, float fromAngle, float tillAngle, float lineWidth ) { if ( fromAngle > tillAngle ) { return; } float dAngle{ radX > radY ? float( g_Pi / radX ) : float( g_Pi / radY ) }; glLineWidth( lineWidth ); glBegin( GL_LINE_STRIP ); { for ( float angle = fromAngle; angle < tillAngle; angle += dAngle ) { glVertex2f( centerX + radX * float( cos( angle ) ), centerY + radY * float( sin( angle ) ) ); } glVertex2f( centerX + radX * float( cos( tillAngle ) ), centerY + radY * float( sin( tillAngle ) ) ); } glEnd( ); } void utils::DrawArc( const Point2f& center, float radX, float radY, float fromAngle, float tillAngle, float lineWidth ) { DrawArc( center.x, center.y, radX, radY, fromAngle, tillAngle, lineWidth ); } void utils::FillArc( float centerX, float centerY, float radX, float radY, float fromAngle, float tillAngle ) { if ( fromAngle > tillAngle ) { return; } float dAngle{ radX > radY ? float( g_Pi / radX ) : float( g_Pi / radY ) }; glBegin( GL_POLYGON ); { glVertex2f( centerX, centerY ); for ( float angle = fromAngle; angle < tillAngle; angle += dAngle ) { glVertex2f( centerX + radX * float( cos( angle ) ), centerY + radY * float( sin( angle ) ) ); } glVertex2f( centerX + radX * float( cos( tillAngle ) ), centerY + radY * float( sin( tillAngle ) ) ); } glEnd( ); } void utils::FillArc( const Point2f& center, float radX, float radY, float fromAngle, float tillAngle ) { FillArc( center.x, center.y, radX, radY, fromAngle, tillAngle ); } void utils::DrawPolygon( const std::vector<Point2f>& vertices, bool closed, float lineWidth ) { DrawPolygon( vertices.data( ), vertices.size( ), closed, lineWidth ); } void utils::DrawPolygon( const Point2f *pVertices, size_t nrVertices, bool closed, float lineWidth ) { glLineWidth( lineWidth ); closed ? glBegin( GL_LINE_LOOP ) : glBegin( GL_LINE_STRIP ); { for ( size_t idx{ 0 }; idx < nrVertices; ++idx ) { glVertex2f( pVertices[idx].x, pVertices[idx].y ); } } glEnd( ); } void utils::FillPolygon( const std::vector<Point2f>& vertices ) { FillPolygon( vertices.data( ), vertices.size( ) ); } void utils::FillPolygon( const Point2f *pVertices, size_t nrVertices ) { glBegin( GL_POLYGON ); { for ( size_t idx{ 0 }; idx < nrVertices; ++idx ) { glVertex2f( pVertices[idx].x, pVertices[idx].y ); } } glEnd( ); } #pragma endregion OpenGLDrawFunctionality #pragma region CollisionFunctionality bool utils::IsPointInRect( const Point2f& p, const Rectf& r ) { return ( p.x >= r.left&& p.x <= r.left + r.width&& p.y >= r.bottom&& p.y <= r.bottom + r.height ); } bool utils::IsPointInCircle( const Point2f& p, const Circlef& c ) { float squaredDist = ( p.x - c.center.x )*( p.x - c.center.x ) + ( p.y - c.center.y ) * ( p.y - c.center.y ); float squaredRadius = c.radius * c.radius; return ( squaredRadius >= squaredDist ); } bool utils::IsOverlapping( const Point2f& a, const Point2f& b, const Rectf& r ) { // if one of the line segment end points is in the rect if ( utils::IsPointInRect( a, r ) || utils::IsPointInRect( b, r ) ) { return true; } HitInfo hitInfo{}; Point2f vertices[]{ Point2f {r.left, r.bottom}, Point2f{ r.left + r.width, r.bottom }, Point2f{ r.left + r.width, r.bottom + r.height }, Point2f{ r.left, r.bottom + r.height } }; return Raycast( vertices, 4, a, b, hitInfo ); } bool utils::IsOverlapping( const Rectf& r1, const Rectf& r2 ) { // If one rectangle is on left side of the other if ( ( r1.left + r1.width ) < r2.left || ( r2.left + r2.width ) < r1.left ) { return false; } // If one rectangle is under the other if ( r1.bottom > ( r2.bottom + r2.height ) || r2.bottom > ( r1.bottom + r1.height ) ) { return false; } return true; } bool utils::IsOverlapping( const Rectf& r, const Circlef& c ) { // Is center of circle in the rectangle? if ( IsPointInRect( c.center, r ) )return true; // Check line segments if ( utils::DistPointLineSegment( c.center, Point2f{ r.left, r.bottom }, Point2f{ r.left, r.bottom + r.height } ) <= c.radius ) return true; if ( utils::DistPointLineSegment( c.center, Point2f{ r.left, r.bottom }, Point2f{ r.left + r.width, r.bottom } ) <= c.radius ) return true; if ( utils::DistPointLineSegment( c.center, Point2f{ r.left + r.width, r.bottom + r.height }, Point2f{ r.left, r.bottom + r.height } ) <= c.radius ) return true; if ( utils::DistPointLineSegment( c.center, Point2f{ r.left + r.width, r.bottom + r.height }, Point2f{ r.left + r.width, r.bottom } ) <= c.radius ) return true; return false; } bool utils::IsOverlapping( const Circlef& c1, const Circlef& c2 ) { // squared distance between centers float xDistance{ c1.center.x - c2.center.x }; float yDistance{ c1.center.y - c2.center.y }; float squaredDistance = xDistance * xDistance + yDistance * yDistance; float squaredTouchingDistance = ( c1.radius + c2.radius ) * ( c1.radius + c2.radius ); if ( squaredDistance < squaredTouchingDistance ) { return true; } else { return false; } } bool utils::IsOverlapping( const Point2f& a, const Point2f& b, const Circlef& c ) { return utils::DistPointLineSegment( c.center, a, b ) <= c.radius; } bool utils::IsOverlapping( const std::vector<Point2f>& vertices, const Circlef& c ) { return IsOverlapping( vertices.data( ), vertices.size( ), c ); } bool utils::IsOverlapping( const Point2f* vertices, size_t nrVertices, const Circlef& c ) { // Check points in circle for ( size_t i{ 0 }; i < nrVertices; ++i ) { if ( IsPointInCircle( vertices[i], c ) ) { return true; } } // Check overlapping line segments with circle for ( size_t i{ 0 }; i < nrVertices; ++i ) { if ( DistPointLineSegment( c.center, vertices[i], vertices[( i + 1 ) % nrVertices] ) <= c.radius ) { return true; } } // No overlapping line segments, verify whether circle is inside polygon if ( IsPointInPolygon( c.center, vertices, nrVertices ) ) { return true; } return false; } bool utils::IsPointInPolygon( const Point2f& p, const std::vector<Point2f>& vertices ) { return IsPointInPolygon( p, vertices.data( ), vertices.size( ) ); } bool utils::IsPointInPolygon( const Point2f& p, const Point2f* vertices, size_t nrVertices ) { if ( nrVertices < 2 ) { return false; } // 1. First do a simple test with axis aligned bounding box around the polygon float xMin{ vertices[0].x }; float xMax{ vertices[0].x }; float yMin{ vertices[0].y }; float yMax{ vertices[0].y }; for ( size_t idx{ 1 }; idx < nrVertices; ++idx ) { if ( xMin > vertices[idx].x ) xMin = vertices[idx].x; if ( xMax < vertices[idx].x ) xMax = vertices[idx].x; if ( yMin > vertices[idx].y ) yMin = vertices[idx].y; if ( yMax < vertices[idx].y ) yMax = vertices[idx].y; } if ( p.x < xMin || p.x > xMax || p.y < yMin || p.y > yMax ) return false; // 2. Draw a virtual ray from anywhere outside the polygon to the point // and count how often it hits any side of the polygon. // If the number of hits is even, it's outside of the polygon, if it's odd, it's inside. int numberOfIntersectionPoints{0}; Point2f p2{ xMax + 10.0f, p.y }; // Horizontal line from point to point outside polygon (p2) // Count the number of intersection points float lambda1{}, lambda2{}; for ( size_t i{ 0 }; i < nrVertices; ++i ) { if ( IntersectLineSegments( vertices[i], vertices[( i + 1 ) % nrVertices], p, p2, lambda1, lambda2 ) ) { if ( lambda1 > 0 && lambda1 <= 1 && lambda2 > 0 && lambda2 <= 1 ) { ++numberOfIntersectionPoints; } } } if ( numberOfIntersectionPoints % 2 == 0 ) return false; else return true; } bool utils::IntersectLineSegments( const Point2f& p1, const Point2f& p2, const Point2f& q1, const Point2f& q2, float& outLambda1, float& outLambda2, float epsilon ) { bool intersecting{ false }; Vector2f p1p2{ p1, p2 }; Vector2f q1q2{ q1, q2 }; // cross product to determine if parallel float denom = p1p2.CrossProduct( q1q2 ); // Don't divide by zero if ( std::abs( denom ) > epsilon ) { intersecting = true; Vector2f p1q1{ p1, q1 }; float num1 = p1q1.CrossProduct( q1q2 ); float num2 = p1q1.CrossProduct( p1p2 ); outLambda1 = num1 / denom; outLambda2 = num2 / denom; } else // are parallel { //connect start points Vector2f p1q1{ p1, q1 }; // cross product to determine if segments and the line connecting their start points are parallel, // if so, than they are on a line // if not, then there is no intersection float denom = p1q1.CrossProduct( q1q2 ); if ( std::abs( denom ) > epsilon ) return false; // check the 4 conditions outLambda1 = 0; outLambda2 = 0; if ( utils::IsPointOnLineSegment( p1, q1, q2 ) )intersecting = true; if ( utils::IsPointOnLineSegment( p2, q1, q2 ) )intersecting = true; if ( utils::IsPointOnLineSegment( q1, p1, p2 ) )intersecting = true; if ( utils::IsPointOnLineSegment( q2, p1, p2 ) )intersecting = true; } return intersecting; } bool utils::Raycast( const std::vector<Point2f>& vertices, const Point2f& rayP1, const Point2f& rayP2, HitInfo& hitInfo ) { return Raycast( vertices.data( ), vertices.size( ), rayP1, rayP2, hitInfo ); } bool utils::Raycast( const Point2f* vertices, const size_t nrVertices, const Point2f& rayP1, const Point2f& rayP2, HitInfo& hitInfo ) { if ( nrVertices == 0 ) { return false; } std::vector<HitInfo> hits; Rectf r1, r2; // r1: minimal AABB rect enclosing the ray r1.left = std::min( rayP1.x, rayP2.x ); r1.bottom = std::min( rayP1.y, rayP2.y ); r1.width = std::max( rayP1.x, rayP2.x ) - r1.left; r1.height = std::max( rayP1.y, rayP2.y ) - r1.bottom; // Line-line intersections. for ( size_t idx{ 0 }; idx <= nrVertices; ++idx ) { // Consider line segment between 2 consecutive vertices // (modulo to allow closed polygon, last - first vertice) Point2f q1 = vertices[( idx + 0 ) % nrVertices]; Point2f q2 = vertices[( idx + 1 ) % nrVertices]; // r2: minimal AABB rect enclosing the 2 vertices r2.left = std::min( q1.x, q2.x ); r2.bottom = std::min( q1.y, q2.y ); r2.width = std::max( q1.x, q2.x ) - r2.left; r2.height = std::max( q1.y, q2.y ) - r2.bottom; if ( IsOverlapping( r1, r2 ) ) { float lambda1{}; float lambda2{}; if ( IntersectLineSegments( rayP1, rayP2, q1, q2, lambda1, lambda2 ) ) { if ( lambda1 > 0&& lambda1 <= 1&& lambda2 > 0&& lambda2 <= 1 ) { HitInfo hitInfo; hitInfo.lambda = lambda1; Point2f intersectPoint{ rayP1.x + ((rayP2.x - rayP1.x) * lambda1), rayP1.y + ((rayP2.y - rayP1.y) * lambda1) }; hitInfo.intersectPoint = intersectPoint; hitInfo.normal = Vector2f{ q2 - q1 }.Orthogonal( ).Normalized( ); hits.push_back( hitInfo ); } } } } if ( hits.size( ) == 0 ) { return false; } // Get closest intersection point and copy it into the hitInfo parameter hitInfo = *std::min_element( hits.begin( ), hits.end( ), []( const HitInfo& first, const HitInfo& last ) { return first.lambda < last.lambda; } ); return true; } bool utils::IsPointOnLineSegment( const Point2f& p, const Point2f& a, const Point2f& b ) { Vector2f ap{ a, p }, bp{ b, p }; // If not on same line, return false if ( abs( ap.CrossProduct( bp ) ) > 0.001f ) { return false; } // Both vectors must point in opposite directions if p is between p1 and p2 if ( ap.DotProduct( bp ) > 0 ) { return false; } return true; } float utils::DistPointLineSegment( const Point2f& p, const Point2f& a, const Point2f& b ) { Vector2f ab{ a, b }; Vector2f ap{ a, p }; Vector2f abNorm = ab.Normalized( ); float distToA = abNorm.DotProduct( ap ); // if distToA is negative, then the closest point is A // return the distance a, p if ( distToA < 0 ) { return ap.Length( ); } // if distToA is > than dist(a,b) then the closest point is B // return the distance b, p float distAB = ab.Length( ); if ( distToA > distAB ) { return Vector2f{ b, p }.Length( ); } //closest point is between A and B, calc intersection point Vector2f intersection = abNorm.DotProduct(ap) * abNorm + Vector2f{ a }; return Vector2f{ p - intersection }.Length( ); } #pragma endregion CollisionFunctionality