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214 Stars 21 Forks BSD 2-Clause "Simplified" License 22 Commits 1 Opened issues


An extension to Core Graphics Geometry. Intersections, scaling, etc.

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An extension to Core Graphics Geometry. Intersections, scaling, etc.


In your Podfile, add this line:

pod "MTGeometry"

pod? =>

NOTE: You may need to add

to "Other Linker Flags" in your targets build settings if the pods library only contains categories.



// Create a delta from x and y deltas
CGDelta CGDeltaMake(CGFloat deltaX, CGFloat deltaY);

// Get the distance between two points CGFloat CGPointDistance(CGPoint p1, CGPoint p2);

// A point along a line distance from point1. CGPoint CGPointAlongLine(CGLine line, CGFloat distance);

// A point rotated around the pivot point by degrees. CGPoint CGPointRotatedAroundPoint(CGPoint point, CGPoint pivot, CGFloat degrees);


// Create a line from 2 points.
CGLine CGLineMake(CGPoint point1, CGPoint point2);

// Returns true if two lines are exactly coincident. bool CGLineEqualToLine(CGLine line1, CGLine line2);

// Get a line's midpoint. CGPoint CGLineMidPoint(CGLine line);

// Get the point at which two lines intersect. Returns NOPOINT if they don't intersect. CGPoint CGLinesIntersectAtPoint(CGLine line1, CGLine line2);

// Get the length of a line. CGFloat CGLineLength(CGLine line);

// Returns a scaled line. Point 1 acts as the anchor and Point 2 is extended. CGLine CGLineScale(CGLine line, CGFloat scale);

// Returns the delta x and y of the line from point 1 to point 2. CGDelta CGLineDelta(CGLine line);


// Corner points of a CGRect
CGPoint CGRectTopLeftPoint(CGRect rect);
CGPoint CGRectTopRightPoint(CGRect rect);
CGPoint CGRectBottomLeftPoint(CGRect rect);
CGPoint CGRectBottomRightPoint(CGRect rect);

// Returns a resized rect with the same centerpoint. CGRect CGRectResize(CGRect rect, CGSize newSize);

// Similar to CGRectInset but only insets one edge. All other edges do not move. CGRect CGRectInsetEdge(CGRect rect, CGRectEdge edge, CGFloat amount);

// Calculates the stacking of rectangles within a larger rectangle. The resulting rectangle is stacked counter clockwise along the edge specified. As soon as there are more rects than will fit, a new row is started, thus, they are stacked by column, then by row. reverse will cause them to be stacked counter-clockwise along the specified edge. CGRect CGRectStackedWithinRectFromEdge(CGRect rect, CGSize size, int count, CGRectEdge edge, bool reverse);

// Find the centerpoint of a rectangle. CGPoint CGRectCenterPoint(CGRect rect);

// Assigns the closest two corner points to point1 and point2 of the rect to the passed in point. void CGRectClosestTwoCornerPoints(CGRect rect, CGPoint point, CGPoint *point1, CGPoint *point2);

// The point at which a line, extended infinitely past its second point, intersects the rectangle. Returns NOPOINT if no intersection is found. CGPoint CGLineIntersectsRectAtPoint(CGRect rect, CGLine line);


// Create a circle from a center and a radius
CGCircle CGCircleMake(CGPoint center, CGFloat radius);

// Returns true if two circles are exactly coincident bool CGCircleEqualToCircle(CGCircle circle1, CGCircle circle2);

// Returns a scaled circle. CGCircle CGCircleScale(CGCircle circle, CGFloat scale);

// Returns a circle translated by delta. CGCircle CGCircleTranslate(CGCircle circle, CGDelta delta);

// Returns true if point is inside or on the boundary of the circle bool CGCircleContainsPoint(CGCircle circle, CGPoint point);

// Returns true if two circles intersect or one is contained within the other bool CGCircleIntersectsCircle(CGCircle circle1, CGCircle circle2);

// Returns true if circle and line intersect bool CGCircleIntersectsLine(CGCircle circle, CGLine line);

// Returns true if circle and rectangle intersect bool CGCircleIntersectsRectangle(CGCircle circle, CGRect rect);

// Returns the minimum size rectangle that contains circle CGRect CGCircleGetBoundingRect(CGCircle circle);

// Returns the distance from a point to a circle // Returns 0 if the point is inside the circle CGFloat CGGetDistanceFromPointToCircle(CGPoint point, CGCircle circle);

Example Usage

Finding the point where two lines intersect:

CGLine line1 = CGLineMake(CGPointMake(2, 0), CGPointMake(2, 4));
CGLine line2 = CGLineMake(CGPointMake(0, 2), CGPointMake(4, 2));
CGLinesIntersectAtPoint(line1, line2)   // => (2,2)

Find the closest two corner points of a rectangle to a point in space:

CGRect rect = CGRectMake(2, 1, 4, 4);
CGPoint point = CGPointMake(0, 0);
CGPoint point1 = CGPointZero;
CGPoint point2 = CGPointZero;
CGRectClosestTwoCornerPoints(rect, point, &point1, &point2);    // => (0,0) (2,1)

The point where a line intersects a rect, if at all:

CGRect rect = CGRectMake(1, 1, 4, 4);
CGLine line = CGLineMake(CGPointMake(0, 1), CGPointMake(2, 2));
CGLineIntersectsRectAtPoint(rect, line);    // => (5, 3.5)

Find if a circle contains a given point:

CGCircle circle = CGCircleMake(CGPointMake(1,2), 3);
CGPoint point = CGPointMake(5,2);
bool containsPoint = CGCircleContainsPoint(circle, point);

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