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12.3.1 Design of the InterpolatorTest example The InterpolatorTestexample creates a Switch Nodeand attaches a SwitchInterpolator. A custom Alphaclass (RandomAlpha) is used to generate Alpha values for the SwitchInterpolator. The RandomAlphagenerates a random Alpha value (between 0 and 1) every 10 seconds. This causes the SwitchInterpolatorto randomly switch between child Nodesevery 10 seconds. The Switch Nodehas six child Nodes: 1. Groupcontaining a ColorInterpolator: Operates on an Appearance. 2. Groupcontaining a PositionInterpolator: Operates on a TransformGroup. 3. Groupcontaining a RotationInterpolator: Operates on a TransformGroup. 4. Groupcontaining a ScaleInterpolator: Operates on a TransformGroup. 5. Groupcontaining a TransparencyInterpolator: Operates on an Appearance. 6. Groupcontaining a RotPosScaleInterpolator: Operates on a TransformGroup. Each Groupalso contains a Link Nodeto a common SharedGroup. The SharedGroupcontains a TransformGroupwith a child Shape3D. The parent TransformGroupis passed to each Interpolatorthat requires a TransformGroup, while the Shape3D s Appearanceis passed to each Interpolatorthat requires an Appearance. A Text2Dis also created with the name of the Interpolatoras text so that the current active Interpolatorcan be seen. See figure 12.4. Figure 12.4 The basic scenegraph design for the InterpolatorTest example The InterpolatorTestexample exploits a useful feature of Behaviors: when the Switchchanges its active child Node, the Behaviorsof the inactive child Nodesare no longer scheduled. In this way, the SwitchInterpolatorthat randomly selects child Nodes(using the RandomAlphaclass) also activates a single Behavior inactive Behaviorsare no longer processed even though they are still enabled. The RandomAlphaclass is very simple: //This class defines an Alpha class that returns //a random value every N milliseconds. 204
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they may be considered to add an additional rotation angle to spherical coordinates: longitude, latitude, and rotation angles. A Quaternion is defined using four floating point values |x y z w|. These are calculated from the combination of the three coordinates of the rotation axis and the rotation angle. Unfortunately most people do not think readily in quaternions, so the following two conversion functions are useful to help create quaternions from axis or Euler angles. The algorithms for the functions were taken from the Matrix and Quaternion FAQ. I encourage you to check the FAQ for updates, optimizations and corrections to this code. From InterpolatorTest.java //Quat4f createQuaternionFromAxisAndAngle //( Vector3d axis, double angle ) { double sin_a = Math.sin( angle / 2 ); double cos_a = Math.cos( angle / 2 ); //use a vector so we can call normalize Vector4f q = new Vector4f(); q.x = (float) (axis.x * sin_a); q.y = (float) (axis.y * sin_a); q.z = (float) (axis.z * sin_a); q.w = (float) cos_a; //It is best to normalize the quaternion //so that only rotation information is used q.normalize(); //convert to a Quat4f and return return new Quat4f( q ); } //Quat4f createQuaternionFromEuler( double angleX, //double angleY, double angleZ ) { //simply call createQuaternionFromAxisAndAngle for each axis //and multiply the results Quat4f qx = createQuaternionFromAxisAndAngle( new Vector3d(1,0,0), angleX ); Quat4f qy = createQuaternionFromAxisAndAngle( new Vector3d(0,1,0), angleY ); Quat4f qz = createQuaternionFromAxisAndAngle( new Vector3d(0,0,1), angleZ ); //qx = qx * qy qx.mul( qy ); //qx = qx * qz qx.mul( qz ); return qx; } 203
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As the name knots implies, a useful way to visualize the interpolator is as a string stretched taut between a number of points. Each point is called a knot, and as well as having an Alpha value (time) when the interpolator is to reach the knot it also possesses position, scale, and rotation information (a pose). The distance between knots defines the speed at which the interpolation between values must occur. Knots are specified using float values between 0 and 1, where 0 is the knot used at Alpha value 0 and 1 is the knot used at Alpha time 1. The array of knot values defines a mapping from Alpha value to pose information. The knot values must increase from 0 to 1 in the knot array. //define the knots array that map from Alpha to pose index float[] knots = {0.0f, 0.1f, 0.2f, 0.3f, 0.4f, 0.6f, 0.8f, 0.9f, 1.0f}; //create array with 9 poses: containing rotation, position //and scale values Quat4f[] quats = new Quat4f[9]; Point3f[] positions = new Point3f[9]; float[] scales = {0.2f, 0.5f, 0.8f, 2.3f, 5.4f, 0.6f, 0.4f, 0.2f, 0.1f}; //define the rotation values for each of the 9 poses quats[0] = new Quat4f(0.3f, 1.0f, 1.0f, 0.0f); quats[1] = new Quat4f(1.0f, 0.0f, 0.0f, 0.3f); quats[2] = new Quat4f(0.2f, 1.0f, 0.0f, 0.0f); quats[3] = new Quat4f(0.0f, 0.2f, 1.0f, 0.0f); quats[4] = new Quat4f(1.0f, 0.0f, 0.4f, 0.0f); quats[5] = new Quat4f(0.0f, 1.0f, 1.0f, 0.2f); quats[6] = new Quat4f(0.3f, 0.3f, 0.0f, 0.0f); quats[7] = new Quat4f(1.0f, 0.0f, 1.0f, 1.0f); quats[8] = quats[0]; //define the positions for each of the 9 poses positions[0]= new Point3f(0.0f, 0.0f, -1.0f); positions[1]= new Point3f(1.0f, -2.0f, -2.0f); positions[2]= new Point3f(-2.0f, 2.0f, -3.0f); positions[3]= new Point3f(1.0f, 1.0f, -4.0f); positions[4]= new Point3f(-4.0f, -2.0f, -5.0f); positions[5]= new Point3f(2.0f, 0.3f, -6.0f); positions[6]= new Point3f(-4.0f, 0.5f, -7.0f); positions[7]= new Point3f(0.0f, -1.5f, -4.0f); positions[8]= positions[0]; //create the interpolator and pass Alpha, TransformGroup, //knots, and pose information RotPosScalePathInterpolator rotPosScalePathInterplator = new RotPosScalePathInterpolator( alpha, tg, new Transform3D(), knots, quats, positions, scales ); As you can see, the rotation angles are specified using the Quat4fclass. The Quat4fclass specifies a rotation as a quaternion. The following is a description of quaternions, taken from the excellent Matrix and Quaternion FAQ. The FAQ can be found online and it currently maintained by Andreas Junghanns at http://www.cs.ualberta.ca/~andreas/math/matrfaq_latest.html. Quaternions extend the concept of rotation in three dimensions to rotation in four dimensions. This avoids the problem of gimbal-lock and allows for the implementation of smooth and continuous rotation. In effect, 202
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//create the Interpolator by default interpolate //between x = 0 and x = 1 Interpolator interpolator = new PositionInterpolator ( alpha, tg ); RotationInterpolator The RotationInterpolatorcan be used to linearly interpolate between two sets of axis angle rotations. The RotationInterpolatormodifies a TransformGroup, which will in turn affect the position of all its child Nodes. The TransformGroupmust have the ALLOW_TRANSFORM_WRITEcapability set. //create the Interpolator by default interpolate //between Y angle = 0 and Y angle = 2p Interpolator interpolator = new RotationInterpolator ( alpha, tg ); ScaleInterpolator The ScaleInterpolatorcan be used to linearly interpolate between two scale values for an axis. The ScaleInterpolatormodifies a TransformGroup, which will in turn affect the position of all its child Nodes. The TransformGroupmust have the ALLOW_TRANSFORM_WRITEcapability set. //create the Interpolator by default interpolate //between a uniform scale of 0 and 1 Interpolator interpolator = new ScaleInterpolator ( alpha, tg ); TransparencyInterpolator The TransparencyInterpolatorcan be used to linearly interpolate between two transparency values. The TransparencyInterpolatormodifies an Appearance s TransparencyAttributes. The TransparencyAttributesmust have the ALLOW_VALUE_WRITEcapability set. //create the TransparencyAttributes TransparencyAttributes transparency = new TransparencyAttributes(); //set the required capability bit transparency.setCapability( TransparencyAttributes.ALLOW_VALUE_WRITE ); //set the transparency mode transparency.setTransparencyMode( TransparencyAttributes.NICEST ); //assign the transparency to an Appearance app.setTransparencyAttributes( transparency ); //create the interpolator and interpolate //between 0 (opaque) and 0.8. Interpolator interpolator = new TransparencyInterpolator( alpha, app.getTransparencyAttributes(), RotPosScalePathInterpolator The RotPosScalePathInterpolatoris the most flexible of all the PathInterpolators. As its name suggests, it allows the rotation, position, and scale of a TransformGroupto be modified. Rotations, positions, and scales are specified at a series of Alpha values (or knots). The rotation, position, and scale defines a pose that, along with the time information, allows the Interpolatorto linearly interpolate between poses based on the Alpha value and the defined knots. 201
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//create the Alpha for the Interpolator Alpha alpha = new Alpha( -1, Alpha.INCREASING_ENABLE | Alpha.DECREASING_ENABLE, 500, 100, 5000, 2000, 1000, 5000, 2000, 500 ); //create the SwitchInterpolator and pass the Alpha //and a Switch Node Interpolator switchInterpolator = new SwitchValueInterpolator( alpha, switchNode ); //add the Interpolator to a parent BranchGroup //and set Scheduling Bounds BranchGroup bg = new BranchGroup(); bg.addChild( interpolator ); interpolator.setSchedulingBounds( getApplicationBounds() ); ColorInterpolator The ColorInterpolatorcan be used to linearly interpolate the Materialdiffuse color of an Appearancebetween two extremes. Note that the Materialmust have the ALLOW_COMPONENT_WRITEcapability bit set. //create an Appearance Appearance app = new Appearance(); //create a Material and assign an initial color Color3f objColor = new Color3f(1.0f, 0.7f, 0.8f); Color3f black = new Color3f(0.0f, 0.0f, 0.0f); Material mat = new Material(objColor, black, objColor, black, 80.0f); //ensure the Interpolator has WRITE access to the Material mat.setCapability( Material.ALLOW_COMPONENT_WRITE ); //assign the Material to the Appearance app.setMaterial( mat ); //create the Interpolator by default interpolate //between black and white Interpolator interpolator = new ColorInterpolator( alpha, app.getMaterial() ); PositionInterpolator The PositionInterpolatorcan be used to linearly interpolate between two x, y, z positions. The PositionInterpolatormodifies a TransformGroup, which will in turn affect the position of all its child Nodes. The TransformGroupmust have the ALLOW_TRANSFORM_WRITEcapability set. //create the TransformGroup TransformGroup tg = new TransformGroup(); tg.setCapability(TransformGroup.ALLOW_TRANSFORM_WRITE); tg.setCapability(TransformGroup.ALLOW_TRANSFORM_READ); 200
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12.2.2 Summary An Alphaclass is very simple it converts a time value in milliseconds to a value between 0 and 1. The built-in Alphaclass defines all the parameters for an Alphafunction to implement a common class of onset, peak, offset activation functions. A custom Alphafunction, such as FileAlpha, is a very powerful mechanism to feed application-specific data into one of the Interpolator-derived classes. An application might define an Alphaclass that samples data straight from a communications port, or reads precomputed data from a file. The output from the custom Alphaclass can then be used to parameterize a wide variety of Interpolators. Alphaclasses are used in conjunction with Interpolators, but they do not do anything visible themselves. Their prime purpose in Java 3D is to provide input to the Interpolatorclasses. Interpolatorsare the subjects of section 12.3, so read on. 12.3 Example of Interpolator usage java.lang.Object | +–javax.media.j3d.SceneGraphObject | +–javax.media.j3d.Node | +–javax.media.j3d.Leaf | +–javax.media.j3d.Behavior | +–javax.media.j3d.Interpolator The Java 3D Interpolatorswere explored using the InterpolatorTestand the SplineInterpolatorTestexamples. The InterpolatorTestexample demonstrates using the following Interpolators: SwitchValueInterpolator The SwitchValueInterpolatoris used to cycle through the children of a Switch Nodebased on the output from an Alphaobject. The SwitchValueInterpolatormaps the output from the Alphainto a current visible child Nodeusing the following algorithm: float f = alpha.value(); int i = firstSwitchIndex + (int)(f * (float)(childCount - 1) + 0.5F); target.setWhichChild(i); Note that the Switch Nodepassed to the SwitchInterpolatormust have the Switch.ALLOW_SWITCH_WRITEcapability. //create the Switch Node Switch switchNode = new Switch(); //set the WRITE capability switchNode.setCapability( Switch.ALLOW_SWITCH_WRITE ); //add children to switchNode here 199
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From the file Values.xls from the CustomAlphaTest example 0 0 1000 0.1 3000 0.4 4000 0.2 6000 0.8 10000 0.5 12000 0.1 14000 1.0 16000 0.1 The text file defines an ordered series of time and alpha value pairs (figure 12.3). Times are specified in milliseconds. The FileAlphaclass overrides the following Alphamethods. public void setStartTime(long l) public long getStartTime() public void setLoopCount( int i ) public int getLoopCount() public boolean finished() public float value( long time ) Please refer to the FileAlphaclass for details. The CustomAlphaTestis also interesting in that it interpolates the position of a ColorCubeusing the FileAlphaand plots the value and time of the FileAlphaon the graph shown in figure 12.3. Figure 12.3 The FileAlpha class loads times and Alpha values from a file and linearly interpolates between them to provide a highly flexible Alpha function 198
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Run the AlphaTest example and interactively modify the nine parameters to get a good feel for how to parameterize an Alphaobject for your application (figure 12.2). Figure 12.2 The AlphaTest example allows an Alpha object to be parameterized interactively and plots the resulting Alpha function While testing the AlphaTest example, I ran into an interesting bug in the Alpha NOTE class. If either the increasing alpha ramp or decreasing alpha ramp parameter is set to zero, the other will also be set to zero. You can work around this bug by setting the parameter to 1 millisecond instead of 0 milliseconds. 12.2.1 Using a custom Alpha class You can, of course, derive your own class from Alphato implement your own Alphafunction. The FileAlphaclass from the CustomAlphaTest examples loads times and alpha values from a text file and linearly interpolates between them. 197
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12.2 The Alpha class java.lang.Object | +–javax.media.j3d.Alpha A good understanding of the Alphaclass is key to using all the Interpolatorbehaviors. The Alpha class defines a function that converts the current time (in milliseconds) to a value between 0 and 1 (alpha value). The alpha value can then be used by the Interpolatorto produce the desired interpolation between specified end states. For example, a PositionInterpolatormight be used to move an object between position (0,0,0) and (0,0,5) in 10 seconds. To achieve the desired result, an Alphaobject must be created that returns 0 at 0 seconds and 1 at 10 seconds. The PositionInterpolatorcan then use the Alphaobject to create the desired z coordinate (table 12.1). Table 12.1 Coordinate calculation using Alpha Time (seconds) Alpha Z Coordinate 0 0 0 * 5 = 0 5 0.5 0.5 * 5 = 2.5 10 1 1 * 5 = 5 The Alphaclass uses a parameterized function to convert time values to alpha values between 0 and 1. Figure 12.1 illustrates the basic shape of the functions that can be created using the Alphaclass. Nine parameters can be used to create a customized Alphafunction are listed there. Figure 12.1 The phases of the Alpha class: triggerTime (1), phase delay (2), increasing alpha (3), increasing alpha ramp (4), at one (5), decreasing alpha (6), decreasing alpha ramp (7), at zero (8), and loopCount (9) The increasing alpha phase (3) is composed of three potential sections, as is the decreasing alpha phase (6). The values of increasing alpha ramp (4) and decreasing alpha ramp (7) define symmetrical acceleration and deceleration of the Alpha value at the beginning and end of the phase. These quadratic sections help to smooth the transition from 0 to 1 (increasing alpha) or 1 to 0 (decreasing alpha). Note that the Alpha value varies linearly between the quadratic sections. The loopCountparameter (9) allows Alphafunctions to be repeated (a fixed number of times or infinitely) by joining Alphafunctions end to end. 196
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CHAPTER 12 Using Interpolator 12.1 The Interpolator class 12.2 The Alpha class 12.3 Example of Interpolator usage 12.4 Using a cubic-spline interpolator 12.5 Summary 219 The Interpolatorclass defines the functionality for an important and powerful set of behaviors that deserve extra mention. The behaviors derived from Interpolatorallow an object s current state to be interpolated between a set of defined states as a function of time. This chapter introduces the Interpolatorclasses and the Alphaclass, which is used to control the speed of interpolation. 12.1 The Interpolator class java.lang.Object | +–javax.media.j3d.SceneGraphObject | +–javax.media.j3d.Node | +–javax.media.j3d.Leaf | +–javax.media.j3d.Behavior | +–javax.media.j3d.Interpolator Java 3D includes a rich set of behaviors for interpolating an object between states. These behaviors are important for many animation and visualization applications and are covered in detail in this section. Interpolatorbehaviors can be used to interpolate an object s: Color Linearly between diffuse material colors Path Position along a specified path Position Linearly between positions Rotation Linearly between rotations Scale Linearly between scale values Switchvalue Toggle Switch Node s visible child based on time Spline path Position along a specified spline path Transparency Linearly between transparency values All the Interpolationclasses require an Alphaobject. The Alphaclass is used to convert the current time to a value between 0 and 1 this value is then used by the Interpolatorto perform its specific action. The Alphaclass is described in section 12.2. 195
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