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Smooth parameteric curve implemented using a piecewise 3rd-order Catmull-Rom spline curve.
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Inherits G3D::SplineBase.
Public Member Functions | |
Spline () | |
Spline (const Control &c) | |
Spline (const Any &any) | |
Accepts a table of properties, or any valid PhysicsFrame specification for a single control. More... | |
void | append (float t, const Control &c) |
Appends a control point at a specific time that must be greater than that of the previous point. More... | |
void | append (const Control &c) |
Appends control point spaced in time based on the previous control point, or spaced at unit intervals if this is the first control point. More... | |
void | clear () |
Erases all control points and times, but retains the state of cyclic and finalInterval. More... | |
void | computeIndex (float s, int &i, float &u) const |
Given a time s, finds i and 0 <= u < 1 such that s = time[i] * u + time[i + 1] * (1 - u). More... | |
float | duration () const |
Returns the amount of time covered by this spline in one period. More... | |
Control | evaluate (float s) const |
Return the position at time s. More... | |
void | getControl (int i, float &t, Control &c) const |
Returns the requested control point and time sample based on array index. More... | |
float | getFinalInterval () const |
See specification for Spline::finalInterval; this handles the non-positive case. More... | |
size_t | hashCode () const |
bool | operator== (const Spline< Control > &other) const |
int | size () const |
Number of control points. More... | |
virtual Any | toAny (const String &myName) const |
Note that invoking classes can call setName on the returned value instead of passing a name in. More... | |
Static Public Member Functions | |
static Matrix4 | computeBasis () |
Computes the derivative spline basis from the control point version. More... | |
Public Attributes | |
Array< Control > | control |
Control points. More... | |
SplineExtrapolationMode | extrapolationMode |
If SplineInterpolationMode::CYCLIC, then the control points will be assumed to wrap around. More... | |
float | finalInterval |
For a cyclic spline, this is the time elapsed between the last control point and the first. More... | |
SplineInterpolationMode | interpolationMode |
Array< float > | time |
Times at which control points occur. More... | |
Protected Member Functions | |
void | computeIndexInBounds (float s, int &i, float &u) const |
Assumes that t0 <= s < tn. More... | |
virtual void | correct (Control &A) const |
Normalize or otherwise adjust this interpolated Control. More... | |
virtual void | ensureShortestPath (Control *A, int N) const |
Mutates the array of N control points that begins at A. More... | |
void | getControls (int i, float *T, Control *A, int N) const |
Returns a series of N control points and times, fixing boundary issues. More... | |
virtual void | init (AnyTableReader &propertyTable) |
Does not invoke verifyDone() on the propertyTable because subclasses may have more properties. More... | |
Protected Attributes | |
Control | zero |
The additive identity control point. More... | |
Smooth parameteric curve implemented using a piecewise 3rd-order Catmull-Rom spline curve.
The spline is considered infinite and may either continue linearly from the specified control points or cycle through them. Control points are spaced uniformly in time at unit intervals by default, but irregular spacing may be explicitly specified.
The dimension of the spline can be set by varying the Control template parameter. For a 1D function, use Spline<float>. For a curve in the plane, Spline<Vector2>. Note that any template parameter that supports operator+(Control) and operator*(float) can be used; you can make splines out of G3D::Vector4, G3D::Matrix3, or your own classes.
To provide shortest-path interpolation, subclass G3D::Spline and override ensureShortestPath(). To provide normalization of interpolated points (e.g., projecting Quats onto the unit hypersphere) override correct().
See Real Time Rendering, 2nd edition, ch 12 for a general discussion of splines and their properties.
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inlineexplicit |
Accepts a table of properties, or any valid PhysicsFrame specification for a single control.
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inline |
Appends a control point at a specific time that must be greater than that of the previous point.
Referenced by G3D::Spline< UprightFrame >::append().
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inline |
Appends control point spaced in time based on the previous control point, or spaced at unit intervals if this is the first control point.
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inline |
Erases all control points and times, but retains the state of cyclic and finalInterval.
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staticinherited |
Computes the derivative spline basis from the control point version.
Referenced by G3D::Spline< UprightFrame >::evaluate().
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inherited |
Given a time s, finds i and 0 <= u < 1 such that s = time[i] * u + time[i + 1] * (1 - u).
Note that i may be outside the bounds of the time and control arrays; use getControl to handle wraparound and extrapolation issues.
This function takes expected O(1) time for control points with uniform time sampled control points or for uniformly distributed random time samples, but may take O( log time.size() ) time in the worst case.
Called from evaluate().
Referenced by G3D::Spline< UprightFrame >::evaluate().
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protectedinherited |
Assumes that t0 <= s < tn.
called by computeIndex.
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inlineprotectedvirtual |
Normalize or otherwise adjust this interpolated Control.
Reimplemented in G3D::PhysicsFrameSpline.
Referenced by G3D::Spline< UprightFrame >::evaluate(), and G3D::Spline< UprightFrame >::getControl().
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inherited |
Returns the amount of time covered by this spline in one period.
For a cyclic spline, this contains the final interval.
Referenced by G3D::Spline< UprightFrame >::getControl().
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inlineprotectedvirtual |
Mutates the array of N control points that begins at A.
It is useful to override this method by one that wraps the values if they are angles or quaternions for which "shortest path" interpolation is significant.
Reimplemented in G3D::UprightSpline, and G3D::PhysicsFrameSpline.
Referenced by G3D::Spline< UprightFrame >::getControls().
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Return the position at time s.
The spline is defined outside of the time samples by extrapolation or cycling.
Referenced by G3D::Entity::SplineTrack::computeFrame().
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Returns the requested control point and time sample based on array index.
If the array index is out of bounds, wraps (for a cyclic spline) or linearly extrapolates (for a non-cyclic spline), assuming time intervals follow the first or last sample recorded.
Calls correct() on the control point if it was extrapolated.
Returns 0 if there are no control points.
Referenced by G3D::Spline< UprightFrame >::getControls().
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inlineprotected |
Returns a series of N control points and times, fixing boundary issues.
The indices may be assumed to be treated cyclically.
Referenced by G3D::Spline< UprightFrame >::evaluate().
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inherited |
See specification for Spline::finalInterval; this handles the non-positive case.
Returns 0 if not cyclic.
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Does not invoke verifyDone() on the propertyTable because subclasses may have more properties.
Referenced by G3D::Spline< UprightFrame >::Spline().
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Number of control points.
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Note that invoking classes can call setName on the returned value instead of passing a name in.
Reimplemented in G3D::UprightSpline, and G3D::PhysicsFrameSpline.
Referenced by G3D::PhysicsFrameSpline::toAny().
Array<Control> G3D::Spline< Control >::control |
Control points.
Must have the same number of elements as Spline::time.
Referenced by G3D::Spline< UprightFrame >::append(), G3D::Spline< UprightFrame >::clear(), G3D::Spline< UprightFrame >::evaluate(), G3D::Spline< UprightFrame >::getControl(), G3D::Spline< UprightFrame >::hashCode(), G3D::Spline< UprightFrame >::init(), G3D::PhysicsFrameSplineEditor::numControlPoints(), G3D::Spline< UprightFrame >::operator==(), G3D::Spline< UprightFrame >::size(), G3D::Spline< UprightFrame >::Spline(), G3D::UprightSplineManipulator::splineSize(), and G3D::Spline< UprightFrame >::toAny().
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inherited |
If SplineInterpolationMode::CYCLIC, then the control points will be assumed to wrap around.
If SplineInterpolationMode::LINEAR, then the tangents at the ends of the spline point to the final control points. If SplineInterpolationMode::CLAMP, the end control points will be treated as multiple contol points (so the value remains constant at the ends)
Referenced by G3D::UprightSplineManipulator::extrapolationMode(), G3D::Spline< UprightFrame >::getControl(), G3D::Spline< UprightFrame >::hashCode(), G3D::Spline< UprightFrame >::init(), G3D::Spline< UprightFrame >::operator==(), G3D::UprightSplineManipulator::setExtrapolationMode(), and G3D::Spline< UprightFrame >::toAny().
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For a cyclic spline, this is the time elapsed between the last control point and the first.
If less than zero this is assumed to be:
(time[0] - time[1] + . time[time.size() - 1] - time[time.size() - 2]) / 2.
Referenced by G3D::Spline< UprightFrame >::hashCode(), G3D::Spline< UprightFrame >::init(), G3D::Spline< UprightFrame >::operator==(), and G3D::Spline< UprightFrame >::toAny().
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inherited |
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inherited |
Times at which control points occur.
Must have the same number of elements as Spline::control.
Referenced by G3D::Spline< UprightFrame >::append(), G3D::Spline< UprightFrame >::clear(), G3D::Spline< UprightFrame >::evaluate(), G3D::Spline< UprightFrame >::getControl(), G3D::Spline< UprightFrame >::hashCode(), G3D::Spline< UprightFrame >::init(), G3D::Spline< UprightFrame >::operator==(), G3D::Spline< UprightFrame >::size(), G3D::Spline< UprightFrame >::Spline(), and G3D::Spline< UprightFrame >::toAny().
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The additive identity control point.
Referenced by G3D::Spline< UprightFrame >::getControl(), and G3D::Spline< UprightFrame >::Spline().