Fengbin: JavaFX Instance (14) "Cubicbeziercurve"

This example shows a three-cubic Bezier curve,in theMathematicalof theNumerical analysisfield,Bezier Curve(English:Bézier curve ) isComputer graphic Scienceis of considerable importance inParametric curve. More HighDimension ofthe extensive Bezier curve is calledBezier surfaces, whereBezier Triangleis a special kind of example. The following are examples of Bezier curves:

linear Bezier Curve

Given the point p_{0,p1, the linear Bezier curve is just a straight line between two points. This line is given by the following formula:}

• 650) this.width=650; "Class=" Mwe-math-fallback-image-inline Tex "alt=" \mathbf{b} (T) =\mathbf{p}_0 + (\mathbf{P}_1-\ MATHBF{P}_0) t= (1-t) \mathbf{p}_0 + t\mathbf{p}_1 \mbox{,} t \in [0,1] "src=" http://upload.wikimedia.org/math/0/5/c/ 05c4210c69ffb1358ceb8eb83a1a06fe.png "style=" border:none;vertical-align:middle; "/>

And it is equivalent to linear interpolation.

two cubic Bezier curve

The path of the quadratic Bezier curve is traced by the_{function B(t) of the given point P 0, p 1, andP2:}

• 650) this.width=650; "Class=" Mwe-math-fallback-image-inline Tex "alt=" \mathbf{b} (t) = (1-T) ^{2}\mathbf{p}_0 + 2t (1-T) \ Mathbf{p}_1 + t^{2}\mathbf{p}_2 \mbox{,} t \in [0,1] "src=" http://upload.wikimedia.org/math/8/a/d/ 8adc5cc34ea9649d6e546043fce9c407.png "style=" border:none;vertical-align:middle; "/>.

The TrueType font uses two Bezier curves that are made of Bézier splines.

Three cubic Bezier curve

P_{0, P P 2, P 34 points in a planar or three-dimensional space define a three-cubic Bezier curve. The curve starts at P 0 toward P 1, and from P 2 's direction came to P 3. Generally do not go through p 1 or P P 0 and P P 3, go to P 2 direction "length how long".}

The parameter form of the curve is:

• 650) this.width=650; "Class=" Mwe-math-fallback-image-inline Tex "alt=" \mathbf{b} (t) =\mathbf{p}_0 (1-T) ^3+3\mathbf{P }_1T (1-t) ^2+3\mathbf{p}_2t^2 (1-t) +\mathbf{p}_3t^3 \mbox{,} t \in [0,1] "src=" HTTP://UPLOAD.WIKIMEDIA.ORG/MATH/5/9/7 /597ecc5022fa7ab65509d5edfa9c148c.png "style=" border:none;vertical-align:middle; "/>

The code for this example is as follows:

Import javafx.application.application;import javafx.scene.scene;import javafx.scene.layout.pane ; import javafx.scene.paint.color;import javafx.stage.stage;import javafx.scene.shape.*;p Ublic  class cubicbeziercurve extends application {  public void start ( Stage primarystage)  {    pane pane = new pane ();        cubiccurve cubiccurve = new cubiccurve ()  ;     cubiccurve.setstartx (    cubiccurve.setstarty);                                    CUBICCURVE.SETCONTROLX1 (; )    cubiccurve.setcontroly1 ( -25);              &nbsP;         CUBICCURVE.SETCONTROLX2 (;    ) Cubiccurve.setcontroly2 (175);                     cubiccurve.setendx (    cubiccurve.setendy); )  ;                                   Cubiccurve.setstroke (Color.Black);      cubiccurve.setstrokewidth (3);      cubiccurve.setfill (Color.White);     pane.getchildren (). Add (CubicCurve);     scene scene =new scene (pane,200,150);     Primarystage.settitle ("Cubicbeziercurve");     primarystage.setscene (Scene);     primarystage.show ();     }} 

The operation results are as follows

650) this.width=650; "src=" Http://s3.51cto.com/wyfs02/M02/53/92/wKioL1RrS3uy26-TAABAfSaHW2w862.jpg "title=" Qq20141118210204.jpg "alt=" Wkiol1rrs3uy26-taabafsahw2w862.jpg "/>

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Fengbin: JavaFX Instance (14) "Cubicbeziercurve"