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Ipelib
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#include <ipegeo.h>
Public Member Functions | |
| Bezier () | |
| Bezier (const Vector &p0, const Vector &p1, const Vector &p2, const Vector &p3) | |
| Vector | point (double t) const |
| Vector | tangent (double t) const |
| double | distance (const Vector &v, double bound) |
| bool | straight (double precision) const |
| void | subdivide (Bezier &l, Bezier &r) const |
| void | approximate (double precision, std::vector< Vector > &result) const |
| Rect | bbox () const |
| bool | snap (const Vector &v, double &t, Vector &pos, double &bound) const |
| void | intersect (const Line &l, std::vector< Vector > &result) const |
| void | intersect (const Segment &l, std::vector< Vector > &result) const |
| void | intersect (const Bezier &b, std::vector< Vector > &result) const |
Static Public Member Functions | |
| static Bezier | quadBezier (const Vector &p0, const Vector &p1, const Vector &p2) |
| static void | oldSpline (int n, const Vector *v, std::vector< Bezier > &result) |
| static void | spline (int n, const Vector *v, std::vector< Bezier > &result) |
| static void | cardinalSpline (int n, const Vector *v, double tension, std::vector< Bezier > &result) |
| static void | spiroSpline (int n, const Vector *v, std::vector< Bezier > &result) |
| static void | closedSpline (int n, const Vector *v, std::vector< Bezier > &result) |
Public Attributes | |
| Vector | iV [4] |
A cubic Bezier spline.
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Default constructor, uninitialized curve.
Referenced by cardinalSpline(), closedSpline(), intersect(), oldSpline(), quadBezier(), spiroSpline(), and spline().
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Constructor with four control points.
References iV.
| Vector Bezier::point | ( | double | t | ) | const |
| Vector Bezier::tangent | ( | double | t | ) | const |
Return tangent direction of curve at parameter t (from 0.0 to 1.0).
The returned vector is not normalized.
References iV.
Referenced by ipe::Snap::setEdge().
| double Bezier::distance | ( | const Vector & | v, |
| double | bound | ||
| ) |
Return distance to Bezier spline.
But may just return bound if actual distance is larger. The Bezier spline is approximated to a precision of 1.0, and the distance to the approximation is returned.
References ipe::Rect::addPoint(), approximate(), ipe::Rect::certainClearance(), and iV.
| bool Bezier::straight | ( | double | precision | ) | const |
Returns true if the Bezier curve is nearly identical to the line segment iV[0]..iV[3].
References ipe::Line::distance(), iV, and ipe::Line::through().
Referenced by approximate(), ipe::Arc::intersect(), intersect(), and snap().
Subdivide this Bezier curve in the middle.
References iV.
Referenced by approximate(), ipe::Arc::intersect(), intersect(), and snap().
| void Bezier::approximate | ( | double | precision, |
| std::vector< Vector > & | result | ||
| ) | const |
Approximate by a polygonal chain.
result must be empty when calling this.
References approximate(), iV, straight(), and subdivide().
Referenced by approximate(), bbox(), and distance().
| Rect Bezier::bbox | ( | ) | const |
Return a tight bounding box (accurate to within 0.5).
References ipe::Rect::addPoint(), approximate(), ipe::Rect::bottomLeft(), iV, and ipe::Rect::topRight().
Referenced by ipe::BBoxPainter::doCurveTo().
Find (approximately) nearest point on Bezier spline.
Find point on spline nearest to v, but only if it is closer than bound. If a point is found, sets t to the parameter value and pos to the actual point, and returns true.
References ipe::Rect::addPoint(), ipe::Rect::certainClearance(), iV, point(), ipe::Vector::snap(), snap(), straight(), and subdivide().
Referenced by ipe::Snap::setEdge(), and snap().
Convert an old-style Ipe B-spline to a series of Bezier splines.
For some reason lost in the mist of time, this was the definition of splines in Ipe for many years. It doesn't use knots. The first and last control point are simply given multiplicity 3.
Bezier splines are appended to result.
References Bezier().
Referenced by ipe::CurveSegment::beziers().
Convert a clamped uniform B-spline to a series of Bezier splines.
See Thomas Sederberg, Computer-Aided Geometric Design, Chapter 6.
In polar coordinates, a control point is defined by three knots, so n control points need n + 2 knots. To clamp the spline to the first and last control point, the first and last knot are repeated three times. This leads to k knot intervals and the knot sequence [0, 0, 0, 1, 2, 3, 4, 5, 6, ..., k-2, k-1, k, k, k] There are k + 5 = n + 2 knots in this sequence, so k = n-3 is the number of knot intervals and therefore the number of output Bezier curves.
If n = 4, the knot sequence is [0, 0, 0, 1, 1, 1] and the result is simply the Bezier curve on the four control points.
When n in {2, 3}, returns a single Bezier curve that is a segment or quadratic Bezier spline. This is different from the behaviour of the "old" Ipe splines.
Bezier splines are appended to result.
References Bezier(), and quadBezier().
Referenced by ipe::CurveSegment::beziers(), and spiroSpline().
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Convert a cardinal spline to a series of Bezier splines.
Bezier splines are appended to result.
References Bezier().
Referenced by ipe::CurveSegment::beziers().
References Bezier(), spline(), ipe::Vector::x, and ipe::Vector::y.
Referenced by ipe::Curve::appendSpiroSpline().
Convert a closed uniform cubic B-spline to a series of Bezier splines.
Bezier splines are appended to result.
References Bezier().
Referenced by ipe::ClosedSpline::beziers().
Compute intersection points of Bezier with Line.
References intersect(), iV, ipe::Line::side(), straight(), and subdivide().
Referenced by intersect().
Compute intersection points of Bezier with Segment.
References Bezier(), ipe::Segment::iP, and ipe::Segment::iQ.
| Vector ipe::Bezier::iV[4] |
Referenced by approximate(), bbox(), Bezier(), ipe::Painter::curveTo(), distance(), ipe::Arc::intersect(), intersect(), ipe::Matrix::operator*(), point(), snap(), straight(), subdivide(), and tangent().