This is a set of Bezier curve functions that deal with Beziers, used by jsPlumb, and perhaps useful for other people. These functions work with Bezier curves of arbitrary degree.
- all input points should be in the format {x:.., y:..}. all output points are in this format too.
- all input curves should be in the format [ {x:.., y:..}, {x:.., y:..}, {x:.., y:..}, {x:.., y:..} ]
- The order of the points is [ start, control point 1, ..., control point N, end ].
locationas used as an input here refers to a decimal in the range [0-1], which indicates a point some proportion along the length of the curve.locationas output has the same format and meaning.
distanceFromCurve(point, curve)
Calculates the distance that the given point lies from the given Bezier. Note that it is computed relative to the center of the Bezier, so if you have stroked the curve with a wide pen you may wish to take that into account! The distance returned is relative to the values of the curve and the point - it will most likely be pixels.
gradientAtPoint(curve, location)
Calculates the gradient to the curve at the given location, as a decimal between 0 and 1 inclusive.
gradientAtPointAlongCurveFrom(location, distance)
Calculates the gradient to the curve at the point which is 'distance' units from the given location. See pointAlongCurveFrom.
nearestPointOnCurve(point, curve)
Calculates the nearest point to the given point on the given curve. The return value of this is a JS object literal, containing both the point's coordinates and also the location of the point (see above), for example:
{ point:{ x:551,y:150 }, location:0.263365 }.
pointOnCurve(curve, location)
Calculates the coordinates of the point on the given Bezier curve at the given location.
pointAlongCurveFrom(curve, location, distance)
Calculates the coordinates of the point on the given curve that is distance units from location. distance should be in the same coordinate space as that used to construct the Bezier curve. For an HTML Canvas usage, for example, distance would be a measure of pixels. The return value is a point in the form:
{ x:..., y:... }
locationAlongCurveFrom(curve, location, distance)
Calculates the location of the point on the given curve that is distance units from location. distance should be in the same coordinate space as that used to construct the Bezier curve. For an HTML Canvas usage, for example, distance would be a measure of pixels. The return value is a float in the range [0,1].
pointAlongCurve(curve, location, distance)
Calculates both the coordinates and location of the point on the given curve that is distance units from location. This function is the function that both locationAlongCurveFrom and pointAlongCurveFrom call. The return value is a JS object containing:
{ point:the new point, location: location in range [0,1], originalPoint:the reference point }
perpendicularToCurveAt(curve, location, length, distance)
Calculates the perpendicular to the given curve at the given location. length is the length of the line you wish for (it will be centered on the point at location). distance is optional, and allows you to specify a point along the path from the given location as the center of the perpendicular returned. The return value of this is an array of two points:
[ {x:...,y:...}, {x:...,y:...} ].