1 Additional 3D Topics Splitting polygons Off screen rendering for capture of rendered images. ...

1Zhang & Liang, Computer Graphics Using Java 2D and 3D (c) 2007 Pearson Education, Inc. All rights reserved.

Additional 3D Topics Splitting polygons Off screen rendering for capture of rendered

images. Sound in Java 3D scene graphs Advanced textures Simple shadows Dynamic geometry change 3D curves and surfaces


Splitting Polygons

We can specify a 3D shape as a collection of polygon faces– In principle, can use any kind of polygon– With more that 3 vertexes, it is possible to have

something that isn't planar– Concave polygons don't necessarily fill

properly Usual practice is to use triangles


Polygons

A convex polygon is one for which– all the interior angles are less than 180 degrees– the interior is entirely to one side of the infinite

extension of any edge– a line connecting any pair of interior points is inside

the polygon.


Splitting a Convex Polygon

Given the vertex list (v1, v2, …, vn) where the vertexes are in counterclockwise order– Create a triangle from the first three vertexes– Remove the middle vertex from the list– Repeat until there are only 3 vertexes left– Create a triangle from the last three vertexes


Concave Poygons Use the angle between each

successive pair of edges to determine if polygon is concave.

Treat each edge as a vector. – Vectors should go in counter-

clockwise Calculate the cross product

for each successive pair of edges.

If any cross product is negative, the polygon is concave.


Splitting Concave Polygons

Find a convex triple in the vertex list by looking for a negative cross product

Extend the first edge of the pair of edges until it intersects another polygon edge. – Form a triangle from the

vertexes that form the second vector and the new point

– Remove the end of the second vector from the vertex list

Repeat until remaining vertexes form convex polygon


Rotational Method for Splitting

For each vertex in order– Move vertex to the origin

– Rotate to put next vertex on x-axis

– If next vertex in sequence is below x-axis, split off a triangle and remove that vertex from list

– Repeat until remaining polygon is convex


Off-Screen rendering What if you want to save or print a rendered scene? Canvas3D supports an off-screen rendering mode To use

– create off-screen canvas– stop the view– attach the off-screen canvas– start the view – render the off-screen buffer– when rendering completes

retrieve the image detach the off-screen buffer


Off-Screen Rendering Create off screen canvas using

public Canvas3D(GraphicsConfiguration gc, boolean offScreen)

Attach to viewview.addCanvas3D(canvas)

Capture imagesImageComponent2D buffer = new ImageComponent2D(ImageComponent.FORMAT_RGB,

bImage);canvas.setOffScreenBuffer(buffer);canvas.renderOffScreenBuffer();canvas.waitForOffScreenRendering();bImage = offScreenCanvas.getOffScreenBuffer().getImage();

OffScreen.java


Sound Sound is often used in applications that use

3D graphics– e.g. games

Java3D has classes to support sound– Added as leaf nodes in scene graphs– Similar to Light


Using Sound: Sound3D.java Create an AudioDevice

su.getViewer.createAudioDevice(); Create a MediaContainer to hold sound data

MediaContainer mc = new MediaContainer(url);

Create a Sound object and add it to the scene graphBackgroundSound sound = new backgroundSound();

sound.setSoundData( mc);sound.setSchedulingBounds( bounds);root.addChild( sound);


3D Texture Mapping

2D texture maps put a 2D image onto a 3D surface– For some surfaces, this may not look very natural

Using a 3D volumetric texture source provides a more natural mapping

Usually use computer-generated textures for this– Procedural textures

There are a few sources of data that provide volumetric data– CAT scans


3D Texture Mapping

Consumes more computing resources in terms of generation and storage of 3D texture data

Realistic texture features of true 3D characteristics can be rendered with relatively simple mapping functions

Texture consists of a 3D array of pixel values Texture coordinates need three values (r, s, t)

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Procedural textures

Often used to simulate natural textures such as marble or wood

Natural textures frequently have some periodic variation associated with them– Not perfectly periodic - need some randomness

imposed onto the periodic behavior


Perlin Noise

Invented by Ken Perlin Widely used for things like fire, smoke, clouds A kind of gradient noise

– Uses a grid of random gradients (unit vectors)

Contribution to noise at x from each neighboring grid point is proportional to the dot product of the gradient and the vector from the grid point to x.


Perlin Noise

Want a function that is smooth and random at the same time– noise(x) is a fractal sum


Example: Marble Texture

Create a marble texture using– sin(x + turbulence(p))

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Bump Mapping

Applying a 2D texture to a surface is not as realistic as a truly textured surface– the normal is constant across a face so the

interaction with light is different Bump mapping uses a varying surface

normal to simulate the effect of a rough surface

http://en.wikipedia.org/wiki/Bump_mapping

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Shadows

Java3D API provides only a local illumination model– Illumination of any object depends only on the

lights and not on any other objects– No shadows or reflections

To compute these kinds of effects need a global illumination model

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Global Illumination Models

Very complex Not practical for real-time rendering Examples

– Ray-tracing– Luminosity


Artificial Shadows

Create a projection of each object to use for the shadow

Similar to a view projection

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Shadow.java

Shadow of a Dodecahedron is projected onto a stone wall– Wall is a texture-mapped rectangle– Gray shadow is just in front of the wall– Shadow is computed when the scene graph is

built

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GeometryChange

Occasionally need to be able to modify actual geometry while the scene graph is live– Shadow of a moving object needs to be

recomputed every time the object moves GeometryUpdater interface provides a

means to do this


Dynamic Geometry Change

Create the geometry with BY_REFERENCE flag set.

Write a class implementing the GeometryUpdater interface. public void updateData(Geometry)

Implement a Behavior class. – Call the GeometryArray method to trigger the update.

public void updateData(GeometryUpdater)


Example: MovingShadows.java

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Curves and Curved Surfaces Java3D doesn't support curves or curved surfaces Parametric equations provide one way to generate

curves and curved surfaces based on a set of equations

More generally, curves and surfaces (in both 2D and 3D) can be specified by a set of points plus a procedure for interpolating between those points– Bezier curves– B-splines

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Types of curves

Bezier curves Spline

– a sequence of smoothly-joined polynomial curves

B-spline – widely used in CG

Bicubic surfaces

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Bezier curves

Bezier curves are defined by a set of control points– Quadratic curves in Java2D are second-order

Bezier curves– Cubic curves in Java2D are third-order Bezier

curves


Bezier Curves General Bezier curve is specified by a set of n

control points

– Bn,i(t) is the Bernstein basis

A third-order Bezier curve has 4 control points

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de Castlejau Algorithm

Allows you to compute a point on a Bezier curve using linear interpolation

Can also be used to subdivide a Bezier curve into segments


deCasteljau Algorithm Start with a sequence of control points

p00, p1

0, p20, p3

0

Compute successively shorter sequencespi

k = (1 - t) pik-1 + t pi+1

k-1

Curve iss(t) = p0

3


Subdivision


BezierCurve.java

Create a LineStripArrary Use deCasteljau algorithm to subdivide the given curve

into shorter segments Subdivide recursively until segments are short enough to

be approximated by a line– Program uses a fixed level of subdivisions

– More generally, use a flatness test


Bezier Surfaces

Create surfaces by extending a Bezier curve along anotherr curve– Tensor product of Bezier curves

Bicubic Bezier surface is the common type– m = n = 3

deCasteljau algorithm can be applied

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Bezier surfaces

Think of surface as family of Bezier curves For a particular value of u, S(v) is a Bezier

curve with control points– for j=0, 1, 2, 3

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BezierSurface.java

Based on a bicubic spline Create a polygon mesh from mxn points Use a TriangleStripArray


The Utah Teapot

A famous object in computer graphics– Constructed by Martin Newell in 1975– Used to test rendering algorithms

Constructed with Bezier patches– Contains 306 vertices defining 32 bicubic

Bezier surface patches

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B-Spline Curves Often used for modeling curved surfaces Also defined by a set of control points

– Doesn't always interpolate the points A set of knot values is used to control

smoothnes and continuity– Uniform B-spline has uniformly-spaced knot

values NURBS : Non-uniform rational B-spline

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B-Spline Curves For B-spline of degree k have

– n+1 control points (p0, p1, …, pn)

– n + k + 2 knots (t0 <= t1 <= …<= tn+k+1)

Nk,i are normalized B-spline blending functions

Curve only defined from [t3 to tn+k-2)

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Cubic B-Spline

Extension of Bezier curves Uniformly distributed knots

– ti+1 - ti = 1, i = 3, 4, …, n Duplicated knots at ends mean force

endpoints to be on the curve– t1 = t2 = t3 = t4

– tn+1 = tn+2 = tn+3 = tn+4

For n=3, this is a cubic Bezier curve

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1 Additional 3D Topics Splitting polygons Off screen rendering for capture of rendered images. ...

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