mirror of
https://gitlab.com/freepascal.org/lazarus/lazarus.git
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1184 lines
29 KiB
XML
1184 lines
29 KiB
XML
<?xml version="1.0" encoding="UTF-8"?>
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<fpdoc-descriptions>
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<package name="lazutils">
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<!--
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====================================================================
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GraphMath
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====================================================================
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-->
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<module name="GraphMath">
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<short>
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A set of mathematical helper routines to simply cross-platform canvas
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drawing.
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</short>
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<descr>
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<p>
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<file>graphmath.pp</file> contains math helper routines for use for
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graphics drawing. It is used to simply cross-platform canvas drawing
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operations. <file>graphmath.pp</file> is part of the <file>LazUtils</file>
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package.
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</p>
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</descr>
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<!-- unresolved references -->
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<element name="Types"/>
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<element name="Classes"/>
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<element name="SysUtils"/>
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<element name="Math"/>
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<element name="LazUtilities"/>
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<element name="TFloatPoint">
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<short>
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<var>TFloatPoint</var> is an extended precision record specifying the X and
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Y coordinates of a point in a graphic environment.
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</short>
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<descr/>
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<seealso/>
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</element>
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<element name="TFloatPoint.X">
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<short>
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Horizontal position for the coordinate.
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</short>
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</element>
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<element name="TFloatPoint.Y">
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<short>
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Vertical position for the coordinate.
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</short>
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</element>
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<element name="TBezier">
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<short>
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Array type used to store the coordinates for Bezier control points as
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floating point values.
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</short>
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<descr>
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<p>
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<var>TBezier</var> allows up to 4 coordinates to be specified which represent
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the control points for the parametric curve. Each coordinate is implemented
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using the TFloatPoint type, and stored as elements in the array.
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</p>
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<p>
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TBezier is the type returned by the Bezier function. The type is passed as an
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argument to routines like: Arc2Bezier, Bezier2Polyline, BezierMidPoint, and
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SplitBezier.
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</p>
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</descr>
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<seealso>
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<link id="Bezier"/>
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<link id="Arc2Bezier"/>
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<link id="Bezier2Polyline"/>
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<link id="BezierMidPoint"/>
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<link id="SplitBezier"/>
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</seealso>
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</element>
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<element name="PPoint">
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<short>
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Pointer to the TPoint type.
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</short>
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<descr/>
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<seealso>
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<link id="#rtl.classes.TPoint">TPoint</link>
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</seealso>
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</element>
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<element name="Angles2Coords">
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<short>
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Converts an Eccentric Angle and an Angle-Length, into the coordinates for
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the Start and End radial Points.
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</short>
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<descr>
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<p>
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Use <var>Angles2Coords</var> to convert an Eccentric (Radial) angle and an
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angle-length, such as are used in X-Windows and GTK, into the coordinates
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for the Start and End radial Points. Like those used in the Arc, Pie, and
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Chord routines from the Windows API.
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</p>
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<p>
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The angles are specified in 1/16th of a degree. For example, a full circle
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equals 5760 (16*360).
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</p>
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<p>
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Positive values in Angle and AngleLength mean counter-clockwise, while
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negative values mean clockwise direction. Zero degrees is at the 3
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o'clock position.
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</p>
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</descr>
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<seealso/>
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</element>
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<element name="Angles2Coords.X">
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<short/>
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</element>
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<element name="Angles2Coords.Y">
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<short/>
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</element>
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<element name="Angles2Coords.Width">
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<short/>
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</element>
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<element name="Angles2Coords.Height">
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<short/>
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</element>
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<element name="Angles2Coords.Angle1">
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<short/>
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</element>
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<element name="Angles2Coords.Angle2">
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<short/>
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</element>
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<element name="Angles2Coords.SX">
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<short/>
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</element>
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<element name="Angles2Coords.SY">
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<short/>
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</element>
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<element name="Angles2Coords.EX">
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<short/>
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</element>
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<element name="Angles2Coords.EY">
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<short/>
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</element>
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<element name="Arc2Bezier">
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<short>
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Converts an Arc and ArcLength into a Bezier Approximation of the Arc.
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</short>
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<descr>
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<p>
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Use <var>Arc2Bezier</var> to convert an Arc and ArcLength into a Bezier
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approximation of the Arc. The Rotation parameter accepts a Rotation-Angle
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for a rotated Ellipse. For a non-rotated ellipse this value would be 0, or
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360. If the AngleLength is greater than 90 degrees, or is equal to 0, it
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automatically exits, as Bezier cannot accurately approximate any angle
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greater then 90 degrees, and in fact for best result no angle greater than
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45 should be converted, instead an array of Bezier's should be created,
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each Bezier describing a portion of the total arc no greater than 45
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degrees.
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</p>
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<p>
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The angles are specified in 1/16th of a degree. For example, a full circle
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equals 5760 (16*360).
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</p>
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<p>
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Positive values in Angle and AngleLength mean counter-clockwise while
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negative values mean clockwise direction. Zero degrees is at the 3
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o'clock position.
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</p>
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</descr>
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<seealso/>
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</element>
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<element name="Arc2Bezier.X">
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<short/>
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</element>
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<element name="Arc2Bezier.Y">
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<short/>
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</element>
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<element name="Arc2Bezier.Width">
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<short/>
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</element>
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<element name="Arc2Bezier.Height">
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<short/>
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</element>
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<element name="Arc2Bezier.Angle1">
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<short/>
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</element>
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<element name="Arc2Bezier.Angle2">
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<short/>
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</element>
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<element name="Arc2Bezier.Rotation">
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<short/>
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</element>
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<element name="Arc2Bezier.Points">
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<short/>
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</element>
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<element name="Bezier">
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<short>
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Gets a TBezier instance representing the specified Bezier control points.
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</short>
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<descr/>
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<seealso/>
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</element>
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<element name="Bezier.Result">
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<short>
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TBezier instance with the values in C1, C2, C3, and C4.
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</short>
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</element>
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<element name="Bezier.C1">
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<short>
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Control point on the parametric curve. C1 is an endpoint.
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</short>
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</element>
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<element name="Bezier.C2">
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<short>
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Control point on the parametric curve. C2 is a directional control point for
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a Quadratic or Cubic Bezier.
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</short>
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</element>
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<element name="Bezier.C3">
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<short>
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Control point on the parametric curve. C3 is a directional control point for
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a Cubic Bezier.
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</short>
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</element>
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<element name="Bezier.C4">
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<short>
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Control point on the parametric curve. C4 is an endpoint.
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</short>
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</element>
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<element name="Bezier2Polyline">
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<short>
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<var>Bezier2Polyline</var> - convert a 4-Point Bezier into a Pointer Array
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of TPoint and a Count variable.
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</short>
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<descr>
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<p>
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Use BezierToPolyline to convert a 4-Point Bezier into a Pointer Array of
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TPoint and a Count variable which can then be used within either a
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Polyline, or Polygon routine. It is primarily for use within
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PolyBezier2Polyline.
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</p>
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<p>
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If Points is not initialized or Count is less then 0, it is set to nil and
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the array starts at 0, otherwise it tries to append points to the array
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starting at Count. Points should ALWAYS be Freed when done by calling to
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ReallocMem(Points, 0) or FreeMem.
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</p>
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</descr>
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<seealso/>
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</element>
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<element name="Bezier2Polyline.Bezier">
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<short/>
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</element>
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<element name="Bezier2Polyline.Points">
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<short/>
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</element>
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<element name="Bezier2Polyline.Count">
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<short/>
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</element>
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<element name="BezierArcPoints">
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<short>
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<var>BezierArcPoints</var> - convert an Arc and ArcLength into a Pointer
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Array of TPoints for use with Polyline or Polygon.
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</short>
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<descr>
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<p>
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Use BezierArcPoints to convert an Arc and ArcLength into a Pointer Array of
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TPoints for use with Polyline or Polygon. The Rotation parameter accepts a
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Rotation-Angle for a rotated Ellipse. For a non-rotated ellipse this value
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would be 0, or 360. The result is an Approximation based on 1 or more
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Beziers.
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</p>
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<p>
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If the AngleLength is greater than 90 degrees, it calls
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PolyBezierArcPoints, otherwise it Converts the angles into a Bezier by
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calling to Arc2Bezier, and then converts the Bezier into an array of Points
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by calling to Bezier2Polyline.
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</p>
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<p>
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The angles are specified in 1/16th of a degree. For example, a full circle
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equals 5760 (16*360).
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</p>
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<p>
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Positive values in Angle and AngleLength mean counter-clockwise while
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negative values mean clockwise direction. Zero degrees is at the 3
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o'clock position.
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|
</p>
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|
<p>
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If Points is not initialized or Count is less then 0, it is set to nil and
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the array starts at 0, otherwise it tries to append points to the array
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starting at Count. Points should ALWAYS be Freed when done by calling
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ReallocMem(Points, 0) or FreeMem.
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</p>
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</descr>
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<seealso/>
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</element>
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<element name="BezierArcPoints.X">
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<short/>
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</element>
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<element name="BezierArcPoints.Y">
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<short/>
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</element>
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<element name="BezierArcPoints.Width">
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<short/>
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</element>
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<element name="BezierArcPoints.Height">
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<short/>
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</element>
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<element name="BezierArcPoints.Angle1">
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<short/>
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</element>
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<element name="BezierArcPoints.Angle2">
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<short/>
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</element>
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<element name="BezierArcPoints.Rotation">
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<short/>
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</element>
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<element name="BezierArcPoints.Points">
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<short/>
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</element>
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<element name="BezierArcPoints.Count">
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<short/>
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</element>
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<element name="BezierMidPoint">
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<short>
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<var>BezierMidPoint</var> - get the Mid-Point of any 4-Point Bezier. It is
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primarily for use in SplitBezier.
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</short>
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<descr/>
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<seealso/>
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</element>
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<element name="BezierMidPoint.Result">
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<short/>
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</element>
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<element name="BezierMidPoint.Bezier">
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<short/>
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</element>
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<element name="CenterPoint">
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<short>
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<var>CenterPoint</var> - get the Center-Point of any rectangle. It is
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primarily for use with, and in, other routines such as Quadrant, and
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RadialPoint.
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</short>
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<descr/>
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<seealso/>
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</element>
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<element name="CenterPoint.Result">
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<short/>
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</element>
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<element name="CenterPoint.Rect">
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<short/>
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</element>
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<element name="CalculateLeftTopWidthHeight">
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<short>
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Calculates the values for the output variables in Left, Top, Width, and Height.
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</short>
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<descr>
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<p>
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<var>CalculateLeftTopWidthHeight</var> checks values in the X1, X2, Y1, and Y2
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arguments and sets the values for the Left, Top, Width, and Height output
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parameters accordingly.
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</p>
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<dl>
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<dt>Left</dt>
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<dd>
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Set to the smaller of the two values in X1 and X2.
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</dd>
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<dt>Width</dt>
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<dd>
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Set to the difference between the X1 and X2 values. The value will be a
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positive integer value or zero (0).
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</dd>
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<dt>Top</dt>
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<dd>
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Set to the smaller of the two values in Y1 and Y2.
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</dd>
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<dt>Height</dt>
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<dd>
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Set to the difference between Y1 and Y2. The value will be a positive integer
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value or zero (0).
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</dd>
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</dl>
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<p>
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Used in the implementation of the Rectangle and Ellipse routines for the GTK
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widgetset.
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</p>
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</descr>
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<version>
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Added in LazUtils version 2.4.0.
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</version>
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<seealso/>
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|
</element>
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|
<element name="CalculateLeftTopWidthHeight.X1">
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|
<short>
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Horizontal coordinate examined in the routine.
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|
</short>
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</element>
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<element name="CalculateLeftTopWidthHeight.Y1">
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<short>
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Vertical coordinate examined in the routine.
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</short>
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</element>
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<element name="CalculateLeftTopWidthHeight.X2">
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<short>
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Horizontal coordinate examined in the routine.
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</short>
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</element>
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<element name="CalculateLeftTopWidthHeight.Y2">
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<short>
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Vertical coordinate examined in the routine.
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</short>
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</element>
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<element name="CalculateLeftTopWidthHeight.Left">
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<short>
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|
Returns the left coordinate for the specified values.
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|
</short>
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|
</element>
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|
<element name="CalculateLeftTopWidthHeight.Top">
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|
<short>
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|
Returns the top coordinate for the specified values.
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|
</short>
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|
</element>
|
|
<element name="CalculateLeftTopWidthHeight.Width">
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|
<short>
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|
Returns the width for the specified horizontal coordinates.
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|
</short>
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|
</element>
|
|
<element name="CalculateLeftTopWidthHeight.Height">
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|
<short>
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|
Returns the height for the specified vertical coordinates.
|
|
</short>
|
|
</element>
|
|
|
|
<element name="Coords2Angles">
|
|
<short>
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|
<var>Coords2Angles</var> - convert the coords for Start and End Radial-
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|
Points into an Eccentric counter clockwise Angle and an Angle-Length.
|
|
</short>
|
|
<descr>
|
|
<p>
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|
Use Coords2Angles to convert the coords for Start and End Radial-Points,
|
|
such as are used in the Windows API Arc Pie and Chord routines, into an
|
|
Eccentric (aka Radial) counter clockwise Angle and an Angle-Length, such as
|
|
are used in X-Windows and GTK.
|
|
</p>
|
|
<p>
|
|
The angles angle1 and angle2 are returned in 1/16th of a degree. For
|
|
example, a full circle equals 5760 (16*360).
|
|
</p>
|
|
<p>
|
|
Zero degrees is at the 3 o'clock position.
|
|
</p>
|
|
</descr>
|
|
<seealso/>
|
|
</element>
|
|
<element name="Coords2Angles.X">
|
|
<short/>
|
|
</element>
|
|
<element name="Coords2Angles.Y">
|
|
<short/>
|
|
</element>
|
|
<element name="Coords2Angles.Width">
|
|
<short/>
|
|
</element>
|
|
<element name="Coords2Angles.Height">
|
|
<short/>
|
|
</element>
|
|
<element name="Coords2Angles.SX">
|
|
<short/>
|
|
</element>
|
|
<element name="Coords2Angles.SY">
|
|
<short/>
|
|
</element>
|
|
<element name="Coords2Angles.EX">
|
|
<short/>
|
|
</element>
|
|
<element name="Coords2Angles.EY">
|
|
<short/>
|
|
</element>
|
|
<element name="Coords2Angles.Angle1">
|
|
<short/>
|
|
</element>
|
|
<element name="Coords2Angles.Angle2">
|
|
<short/>
|
|
</element>
|
|
|
|
<element name="Distance">
|
|
<short>
|
|
Get the <var>Distance</var> between any two Points. It is primarily for use
|
|
in other routines such as EccentricAngle.
|
|
</short>
|
|
<descr/>
|
|
<seealso/>
|
|
</element>
|
|
<element name="Distance.Result">
|
|
<short/>
|
|
</element>
|
|
<element name="Distance.PT1">
|
|
<short/>
|
|
</element>
|
|
<element name="Distance.Pt2">
|
|
<short/>
|
|
</element>
|
|
|
|
<element name="EccentricAngle">
|
|
<short>
|
|
<var>EccentricAngle</var> - get the Eccentric Angle of a given point on any
|
|
non-rotated ellipse.
|
|
</short>
|
|
<descr>
|
|
<p>
|
|
Use EccentricAngle to get the Eccentric( aka Radial ) Angle of a given
|
|
point on any non-rotated ellipse. It is primarily for use in Coords2Angles.
|
|
The result is in 1/16th of a degree. For example, a full circle equals 5760
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|
(16*360). Zero degrees is at the 3 o'clock position.
|
|
</p>
|
|
</descr>
|
|
<seealso/>
|
|
</element>
|
|
<element name="EccentricAngle.Result">
|
|
<short/>
|
|
</element>
|
|
<element name="EccentricAngle.PT">
|
|
<short/>
|
|
</element>
|
|
<element name="EccentricAngle.Rect">
|
|
<short/>
|
|
</element>
|
|
|
|
<element name="EllipseRadialLength">
|
|
<short>
|
|
<var>EllipseRadialLength</var> - Radial-Length of non-rotated ellipse at
|
|
any given Eccentric Angle.
|
|
</short>
|
|
<descr>
|
|
<p>
|
|
Use EllipseRadialLength to get the Radial-Length of non-rotated ellipse at
|
|
any given Eccentric( aka Radial ) Angle. It is primarily for use in other
|
|
routines such as RadialPoint. The Eccentric angle is in 1/16th of a degree.
|
|
For example, a full circle equals 5760 (16*360). Zero degrees is at the 3
|
|
o'clock position.
|
|
</p>
|
|
</descr>
|
|
<seealso/>
|
|
</element>
|
|
<element name="EllipseRadialLength.Result">
|
|
<short/>
|
|
</element>
|
|
<element name="EllipseRadialLength.Rect">
|
|
<short/>
|
|
</element>
|
|
<element name="EllipseRadialLength.EccentricAngle">
|
|
<short/>
|
|
</element>
|
|
|
|
<element name="FloatPoint">
|
|
<short>
|
|
<var>FloatPoint</var> - it is essentially like Classes.Point in use, except
|
|
that it accepts Extended Parameters. It is Primarily for use with and in
|
|
Bezier routines.
|
|
</short>
|
|
<descr/>
|
|
<seealso/>
|
|
</element>
|
|
<element name="FloatPoint.Result">
|
|
<short/>
|
|
</element>
|
|
<element name="FloatPoint.AX">
|
|
<short/>
|
|
</element>
|
|
<element name="FloatPoint.AY">
|
|
<short/>
|
|
</element>
|
|
|
|
<element name="LineEndPoint">
|
|
<short>
|
|
<var>LineEndPoint</var> - get the End-Point of a line of any given Length
|
|
at any given angle with any given Start-Point.
|
|
</short>
|
|
<descr>
|
|
<p>
|
|
Use LineEndPoint to get the End-Point of a line of any given Length at any
|
|
given angle with any given Start-Point. It is primarily for use in other
|
|
routines such as RadialPoint. The angle is in 1/16th of a degree. For
|
|
example, a full circle equals 5760 (16*360). Zero degrees is at the 3
|
|
o'clock position.
|
|
</p>
|
|
</descr>
|
|
<seealso/>
|
|
</element>
|
|
<element name="LineEndPoint.Result">
|
|
<short/>
|
|
</element>
|
|
<element name="LineEndPoint.StartPoint">
|
|
<short/>
|
|
</element>
|
|
<element name="LineEndPoint.Angle">
|
|
<short/>
|
|
</element>
|
|
<element name="LineEndPoint.Length">
|
|
<short/>
|
|
</element>
|
|
|
|
<element name="MakeMinMax">
|
|
<short>
|
|
Ensures that the i1 argument is the smaller of the two Integer values.
|
|
</short>
|
|
<descr>
|
|
<p>
|
|
<var>MakeMinMax</var> swaps the values in i1 and i2 variable parameters when
|
|
i1 is larger than i2. No actions are performed in the routine if i1 is smaller
|
|
than i2, or the arguments have the same value.
|
|
</p>
|
|
</descr>
|
|
<version>
|
|
Added in LazUtils version 2.4.0.
|
|
</version>
|
|
<seealso/>
|
|
</element>
|
|
<element name="MakeMinMax.i1">
|
|
<short>
|
|
Integer value compared (and potentially updated) in the routine.
|
|
</short>
|
|
</element>
|
|
<element name="MakeMinMax.i2">
|
|
<short>
|
|
Integer value compared (and potentially updated) in the routine.
|
|
</short></element>
|
|
|
|
<element name="MoveRect">
|
|
<short>
|
|
Moves the specified rectangle to the origin in the x and y arguments.
|
|
</short>
|
|
<descr>
|
|
<p>
|
|
<var>MoveRect</var> sets the Left and Top members in ARect to the values
|
|
specified in x and y (respectively). The Right and Bottom members in ARect are
|
|
updated to reflect the relative distance from the original Top and Left on
|
|
entry.
|
|
</p>
|
|
</descr>
|
|
<version>
|
|
Added in LazUtils version 2.4.0.
|
|
</version>
|
|
<seealso/>
|
|
</element>
|
|
<element name="MoveRect.ARect">
|
|
<short>
|
|
TRect instance updated in the routine.
|
|
</short>
|
|
</element>
|
|
<element name="MoveRect.x">
|
|
<short>
|
|
New position for the Top coordinate in the rectangle.
|
|
</short>
|
|
</element>
|
|
<element name="MoveRect.y">
|
|
<short>
|
|
New position for the Left coordinate in the rectangle.
|
|
</short>
|
|
</element>
|
|
|
|
<element name="MoveRectToFit">
|
|
<short>
|
|
Moves and potentially resizes a rectangle to fit within the specified target
|
|
rectangle.
|
|
</short>
|
|
<descr>
|
|
<p>
|
|
<var>ARect</var> is the TRect instance repositioned in the routine. Values in
|
|
the Left, Right, Top, and Bottom members may be updated in the routine if the
|
|
rectangle is not located within the bounds for the target rectangle.
|
|
</p>
|
|
<p>
|
|
<var>MaxRect</var> is the TRectangle instance where ARect is repositioned. It
|
|
also establishes the maximum size for ARect after it has been repositioned. If
|
|
aRect is larger than MaxRect, ARect is resized to fit with in the constraints
|
|
in MaxRect.
|
|
</p>
|
|
<p>
|
|
MoveRectToFit is used in the implementation for the DoDock method in TControl.
|
|
</p>
|
|
</descr>
|
|
<version>
|
|
Added in LazUtils version 2.4.0.
|
|
</version>
|
|
<seealso/>
|
|
</element>
|
|
<element name="MoveRectToFit.ARect">
|
|
<short>
|
|
TRect instance moved and optionally resized in the routine.
|
|
</short>
|
|
</element>
|
|
<element name="MoveRectToFit.MaxRect">
|
|
<short>
|
|
TRect instance where the rectangle is relocated. It also specifies the maximum
|
|
size for the relocated rectangle.
|
|
</short>
|
|
</element>
|
|
|
|
<element name="PolyBezier2Polyline">
|
|
<short>
|
|
<var>PolyBezier2Polyline</var> - convert an array of 4-Point Bezier into a
|
|
Pointer Array of TPoint and a Count variable.
|
|
</short>
|
|
<descr>
|
|
<p>
|
|
Use BezierToPolyline to convert an array of 4-Point Bezier into a Pointer
|
|
Array of TPoint and a Count variable which can then be used within either a
|
|
Polyline, or Polygon routine. Points is automatically initialized, so any
|
|
existing information is lost, and the array starts at 0. Points should
|
|
ALWAYS be Freed when done by calling to ReallocMem(Points, 0).
|
|
</p>
|
|
</descr>
|
|
<seealso/>
|
|
</element>
|
|
<element name="PolyBezier2Polyline.Beziers">
|
|
<short/>
|
|
</element>
|
|
<element name="PolyBezier2Polyline.Points">
|
|
<short/>
|
|
</element>
|
|
<element name="PolyBezier2Polyline.Count">
|
|
<short/>
|
|
</element>
|
|
|
|
<element name="PolyBezierArcPoints">
|
|
<short>
|
|
<var>PolyBezierArcPoints</var> - convert an Arc and ArcLength into a
|
|
Pointer Array of TPoints for use with Polyline or Polygon.
|
|
</short>
|
|
<descr>
|
|
<p>
|
|
Use PolyBezierArcPoints to convert an Arc and ArcLength into a Pointer
|
|
Array of TPoints for use with Polyline or Polygon. The Rotation parameter
|
|
accepts a Rotation-Angle for a rotated Ellipse - for a non-rotated ellipse
|
|
this value would be 0, or 360. The result is an Approximation based on 1 or
|
|
more Beziers. If the AngleLength is greater than 45 degrees, it recursively
|
|
breaks the Arc into Arcs of 45 degrees or less, and converts them into
|
|
Beziers with BezierArcPoints.
|
|
</p>
|
|
<p>
|
|
The angles are specified in 1/16th of a degree. For example, a full circle
|
|
equals 5760 (16*360).
|
|
</p>
|
|
<p>
|
|
Positive values in Angle and AngleLength mean counter-clockwise while
|
|
negative values mean clockwise direction. Zero degrees is at the 3
|
|
o'clock position.
|
|
</p>
|
|
<p>
|
|
Points is automatically initialized, so any existing information is lost,
|
|
and the array starts at 0. Points should ALWAYS be Freed when done by
|
|
calling to ReallocMem(Points, 0).
|
|
</p>
|
|
</descr>
|
|
<seealso/>
|
|
</element>
|
|
<element name="PolyBezierArcPoints.X">
|
|
<short/>
|
|
</element>
|
|
<element name="PolyBezierArcPoints.Y">
|
|
<short/>
|
|
</element>
|
|
<element name="PolyBezierArcPoints.Width">
|
|
<short/>
|
|
</element>
|
|
<element name="PolyBezierArcPoints.Height">
|
|
<short/>
|
|
</element>
|
|
<element name="PolyBezierArcPoints.Angle1">
|
|
<short/>
|
|
</element>
|
|
<element name="PolyBezierArcPoints.Angle2">
|
|
<short/>
|
|
</element>
|
|
<element name="PolyBezierArcPoints.Rotation">
|
|
<short/>
|
|
</element>
|
|
<element name="PolyBezierArcPoints.Points">
|
|
<short/>
|
|
</element>
|
|
<element name="PolyBezierArcPoints.Count">
|
|
<short/>
|
|
</element>
|
|
|
|
<element name="Quadrant">
|
|
<short>
|
|
Determine the <var>Quadrant</var> of any point, given the Center.
|
|
</short>
|
|
<descr>
|
|
<p>
|
|
Use Quadrant to determine the Quadrant of any point, given the Center. It
|
|
is primarily for use in other routines such as EccentricAngle. A result of
|
|
1-4 represents the primary 4 quadrants. A result of 5-8 means the point
|
|
lies on one of the Axis, 5 = -Y Axis, 6 = +X Axis, 7 = +Y Axis, and 8 = -X
|
|
Axis. A result of -1 means that it does not fall in any quadrant, that is,
|
|
it is the Center.
|
|
</p>
|
|
</descr>
|
|
<seealso/>
|
|
</element>
|
|
<element name="Quadrant.Result">
|
|
<short/>
|
|
</element>
|
|
<element name="Quadrant.PT">
|
|
<short/>
|
|
</element>
|
|
<element name="Quadrant.Center">
|
|
<short/>
|
|
</element>
|
|
|
|
<element name="RadialPoint">
|
|
<short>
|
|
Get the <var>RadialPoint</var> at any given Eccentric angle on any non-
|
|
rotated ellipse.
|
|
</short>
|
|
<descr>
|
|
<p>
|
|
Use RadialPoint to get the Radial-Point at any given Eccentric(aka Radial)
|
|
angle on any non-rotated ellipse. It is primarily for use in Angles2Coords.
|
|
The EccentricAngle is in 1/16th of a degree. For example, a full circle
|
|
equals 5760 (16*360). Zero degrees is at the 3 o'clock position.
|
|
</p>
|
|
</descr>
|
|
<seealso/>
|
|
</element>
|
|
<element name="RadialPoint.Result">
|
|
<short/>
|
|
</element>
|
|
<element name="RadialPoint.EccentricAngle">
|
|
<short/>
|
|
</element>
|
|
<element name="RadialPoint.Rect">
|
|
<short/>
|
|
</element>
|
|
|
|
<element name="RotatePoint">
|
|
<short>
|
|
Rotates a point around the origin by the specified angle (in radians).
|
|
</short>
|
|
<descr>
|
|
<p>
|
|
Rotates a point around the origin (0,0) by the angle in AAngle. The angle is
|
|
in radians and positive for counter-clockwise rotation.
|
|
Note that y points downwards.
|
|
</p>
|
|
</descr>
|
|
<seealso/>
|
|
</element>
|
|
<element name="RotatePoint.Result">
|
|
<short>TPoint with the coordinates after rotation.</short>
|
|
</element>
|
|
<element name="RotatePoint.APoint">
|
|
<short>TPoint with coordinates rotated in the routine.</short>
|
|
</element>
|
|
<element name="RotatePoint.AAngle">
|
|
<short>Rotation angle in radians.</short>
|
|
</element>
|
|
|
|
<element name="RotateRect">
|
|
<short>
|
|
Rotates a rectangle with the specified dimensions by the specified angle
|
|
(in radians).
|
|
</short>
|
|
<descr>
|
|
<p>
|
|
Rotates the rectangle (0, 0, AWidth, AHeight) around its top-left corner
|
|
(0,0) by the angle in AAngle (in radians).
|
|
Note that y points downwards.
|
|
</p>
|
|
</descr>
|
|
<seealso/>
|
|
</element>
|
|
<element name="RotateRect.Result">
|
|
<short>The smallest TRect which contains the rotated rectangle.</short>
|
|
</element>
|
|
<element name="RotateRect.AWidth">
|
|
<short>Width for the rectangle.</short>
|
|
</element>
|
|
<element name="RotateRect.AHeight">
|
|
<short>Height for the rectangle.</short>
|
|
</element>
|
|
<element name="RotateRect.AAngle">
|
|
<short>Rotation angle in radians.</short>
|
|
</element>
|
|
|
|
<element name="SplitBezier">
|
|
<short>
|
|
<var>SplitBezier</var> - split any 4-Point Bezier into two 4-Point Beziers:
|
|
a 'Left' and a 'Right'
|
|
</short>
|
|
<descr>
|
|
<p>
|
|
Use SplitBezier to split any 4-Point Bezier into two 4-Point Beziers: a
|
|
'Left' and a 'Right'. It is primarily for use in Bezier2Polyline.
|
|
</p>
|
|
</descr>
|
|
<seealso/>
|
|
</element>
|
|
<element name="SplitBezier.Bezier">
|
|
<short/>
|
|
</element>
|
|
<element name="SplitBezier.Left">
|
|
<short/>
|
|
</element>
|
|
<element name="SplitBezier.Right">
|
|
<short/>
|
|
</element>
|
|
|
|
<element name="add(TFloatPoint,TFloatPoint):TFloatPoint">
|
|
<short>
|
|
Implements the Add operator (+) for values using the TFloatPoint type.
|
|
</short>
|
|
<descr>
|
|
<p>
|
|
Values for the X and Y members in the addends are summed and stored in the
|
|
corresponding members in the TFloatPoint result.
|
|
</p>
|
|
</descr>
|
|
</element>
|
|
|
|
<element name="add(TFloatPoint,Extended):TFloatPoint">
|
|
<short>
|
|
Implements the Add operator (+) for values using the TFloatPoint and Extended
|
|
types.
|
|
</short>
|
|
<descr>
|
|
<p>
|
|
The Extended value is added to both the X and Y members in the TFloatPoint
|
|
type and used in the result for the operator.
|
|
</p>
|
|
</descr>
|
|
<seealso/>
|
|
</element>
|
|
|
|
<element name="add(Extended,TFloatPoint):TFloatPoint">
|
|
<short>
|
|
Implements the Add operator (+) for values using the Extended and TFloatPoint
|
|
types.
|
|
</short>
|
|
<descr>
|
|
<p>
|
|
The Extended value is added to both the X and Y members in the TFloatPoint
|
|
type and used in the result for the operator.
|
|
</p>
|
|
</descr>
|
|
<seealso/>
|
|
</element>
|
|
|
|
<element name="add(TFloatPoint,TPoint):TFloatPoint">
|
|
<short>
|
|
Implements the Add operator (+) for values using the TFloatPoint and TPoint
|
|
types.
|
|
</short>
|
|
<descr/>
|
|
<seealso/>
|
|
</element>
|
|
|
|
<element name="add(TPoint,TFloatPoint):TFloatPoint">
|
|
<short>
|
|
Implements the Add operator (+) for values using the TPoint and TFloatPoint
|
|
types.
|
|
</short>
|
|
<descr/>
|
|
<seealso/>
|
|
</element>
|
|
|
|
<element name="subtract(TFloatPoint,Extended):TFloatPoint">
|
|
<short>
|
|
Implements the Subtract operator (-) for values using the TFloatPoint and
|
|
Extended types.
|
|
</short>
|
|
<descr>
|
|
<p>
|
|
The value in the Extended type is subtracted from both the X and Y members in
|
|
the TFloatPoint type and used in the result for the operator.
|
|
</p>
|
|
</descr>
|
|
</element>
|
|
|
|
<element name="subtract(TFloatPoint,TFloatPoint):TFloatPoint">
|
|
<short>
|
|
Implements the Subtract operator (-) for values using the TFloatPoint type.
|
|
</short>
|
|
<descr/>
|
|
</element>
|
|
|
|
<element name="subtract(TFloatPoint,TPoint):TFloatPoint">
|
|
<short>
|
|
Implements the Subtract operator (-) for values using the TFloatPoint and
|
|
TPoint types.
|
|
</short>
|
|
<descr/>
|
|
</element>
|
|
|
|
<element name="subtract(TPoint,TFloatPoint):TFloatPoint">
|
|
<short>
|
|
Implements the Subtract operator (-) for values using the TPoint and
|
|
TFloatPoint types.
|
|
</short>
|
|
<descr/>
|
|
</element>
|
|
|
|
<element name="multiply(TFloatPoint,TFloatPoint):TFloatPoint">
|
|
<short>
|
|
Implements the Multiply operator (*) for values using the TFloatPoint type.
|
|
</short>
|
|
<descr/>
|
|
</element>
|
|
|
|
<element name="multiply(TFloatPoint,Extended):TFloatPoint">
|
|
<short>
|
|
Implements the Multiply operator (*) for values using the TFloatPoint and
|
|
Extended types.
|
|
</short>
|
|
<descr>
|
|
<p>
|
|
The value in the Extended type is applied to both the X and Y members in the TFloatPoint type and used in the result for the operator.
|
|
</p>
|
|
</descr>
|
|
</element>
|
|
|
|
<element name="multiply(Extended,TFloatPoint):TFloatPoint">
|
|
<short>
|
|
Implements the Multiply operator (*) for values using the Extended and
|
|
TFloatPoint types.
|
|
</short>
|
|
<descr>
|
|
<p>
|
|
The value in the Extended type is applied to both the X and Y members in the TFloatPoint type and used in the result for the operator.
|
|
</p>
|
|
</descr>
|
|
</element>
|
|
|
|
<element name="multiply(TFloatPoint,TPoint):TFloatPoint">
|
|
<short>
|
|
Implements the Multiply operator (*) for values using the TFloatPoint and
|
|
TPoint types.
|
|
</short>
|
|
<descr/>
|
|
</element>
|
|
|
|
<element name="multiply(TPoint,TFloatPoint):TFloatPoint">
|
|
<short>
|
|
Implements the Multiply operator (*) for values using the TPoint and
|
|
TFloatPoint types.
|
|
</short>
|
|
<descr/>
|
|
</element>
|
|
|
|
<element name="divide(TFloatPoint,TFloatPoint):TFloatPoint">
|
|
<short>
|
|
Implements the Divide operator (/) for values using the TFloatPoint type.
|
|
</short>
|
|
<descr/>
|
|
</element>
|
|
|
|
<element name="divide(TFloatPoint,Extended):TFloatPoint">
|
|
<short>
|
|
Implements the Divide operator (/) for values using the TFloatPoint and
|
|
Extended types.
|
|
</short>
|
|
<descr>
|
|
<p>
|
|
The value in the Extended type is applied to both the X and Y members in the
|
|
TFloatPoint type and used in the result for the operator. No validation is
|
|
performed for the divisor in the operator.
|
|
</p>
|
|
</descr>
|
|
</element>
|
|
|
|
<element name="divide(TFloatPoint,TPoint):TFloatPoint">
|
|
<short>
|
|
Implements the Divide operator (/) for values using the TFloatPoint and
|
|
TPoint types.
|
|
</short>
|
|
<descr/>
|
|
</element>
|
|
|
|
<element name="divide(TPoint,TFloatPoint):TFloatPoint">
|
|
<short>
|
|
Implements the Divide operator (/) for values using the TPoint and
|
|
TFloatPoint types.
|
|
</short>
|
|
<descr/>
|
|
</element>
|
|
|
|
<element name="equal(TPoint,TPoint):Boolean">
|
|
<short>
|
|
Implements the Equal operator (=) to compare values using the TPoint type.
|
|
</short>
|
|
<descr>
|
|
<p>
|
|
The result is <b>True</b> when the X and Y members in the compared values are
|
|
the same.
|
|
</p>
|
|
</descr>
|
|
</element>
|
|
|
|
<element name="equal(TFloatPoint,TFloatPoint):Boolean">
|
|
<short>
|
|
Implements the Equal operator (=) to compare values using the TFloatPoint type.
|
|
</short>
|
|
<descr>
|
|
<p>
|
|
The result is <b>True</b> when the X and Y members in the compared values are
|
|
the same.
|
|
</p>
|
|
</descr>
|
|
</element>
|
|
|
|
<element name="equal(TRect,TRect):Boolean">
|
|
<short>
|
|
Implements the Equal operator (=) to compare values using the TRect type.
|
|
</short>
|
|
<descr>
|
|
<p>
|
|
The result is <b>True</b> when the Left, Top, Right, and Bottom members in the
|
|
compared values are the same.
|
|
</p>
|
|
</descr>
|
|
</element>
|
|
|
|
<element name="assign(TFloatPoint):TPoint">
|
|
<short>
|
|
Implements the Assign operator (=) to store a value using the TFloatPoint type
|
|
to a TPoint instance.
|
|
</short>
|
|
<descr>
|
|
<p>
|
|
<var>SimpleRoundTo</var> in the RTL <file>math.pp</file> unit is called to
|
|
round both the X and Y members to a Double value with 0 decimals in the
|
|
precision. The Double values are truncated and stored to the Longint types
|
|
used for the X and Y members in the result for the operator.
|
|
</p>
|
|
</descr>
|
|
</element>
|
|
|
|
<element name="assign(TPoint):TFloatPoint">
|
|
<short>
|
|
Implements the Assign operator (=) to store a value using the TPoint type to a
|
|
TFloatPoint instance.
|
|
</short>
|
|
<descr/>
|
|
</element>
|
|
|
|
<topic name="GraphMathOperators">
|
|
<short>
|
|
<b>GraphMath Operators</b>.
|
|
</short>
|
|
<descr>
|
|
<p>
|
|
This Unit contains a number of routines for calculating and converting
|
|
series of graphic points from one coordinate system to another.
|
|
</p>
|
|
<p>
|
|
A fundamental type is introduced, called TFloatPoint. It is an extended
|
|
precision record containing an X and a Y coordinate for a graphic point.
|
|
Its structure is as follows:
|
|
</p>
|
|
<code>
|
|
type
|
|
TFloatPoint = record
|
|
X, Y: Extended;
|
|
end;
|
|
</code>
|
|
<p>
|
|
The Unit contains definitions for mathematical operators which extend the
|
|
normal definitions of addition, subtraction, multiplication, division and
|
|
comparison to cover manipulations with TFloatPoints, allowing, for example,
|
|
addition or multiplication of two TFloatPoints, a TFloatPoint and a TPoint,
|
|
or a TFloatPoint and an Extended precision number.
|
|
</p>
|
|
</descr>
|
|
</topic>
|
|
</module>
|
|
<!-- GraphMath -->
|
|
</package>
|
|
</fpdoc-descriptions>
|