threeD.raytracer.primitives
Class Polynomial

java.lang.Object
  threeD.raytracer.engine.AbstractSurface
      threeD.raytracer.primitives.Polynomial

All Implemented Interfaces:

Surface

public class Polynomial

extends AbstractSurface

A Polynomial object represents a 3d polynomial surface.

Constructor Summary

Polynomial()
Constructs a new Polynomial object with no terms.

Polynomial(PolynomialTerm[] terms)
Constructs a new Polynomial object with the specified terms.

Method Summary

Polynomial	add(Polynomial polynomial) Combines the terms of this Polynomial object and the specified Polynomial object and returns the sum as a Polynomial object.
void	addTerm(PolynomialTerm term) Adds the specified PolynomialTerm object to this Polynomial object.
void	calculateDx() Calculates the terms of the partial derivative of the polynomial function represented by this Polynomial object with respect to X and stores the terms for later evaluatation.
void	calculateDy() Calculates the terms of the partial derivative of the polynomial function represented by this Polynomial object with respect to Y and stores the terms for later evaluatation.
void	calculateDz() Calculates the terms of the partial derivative of the polynomial function represented by this Polynomial object with respect to Z and stores the terms for later evaluatation.
double	calculateZero(double initialValue, double yValue, double zValue, int recursions) Calculates an estimate for an X value that allows the polynomial function represented by this Polynomial object to equal zero when the specified Y and Z values are held constant.
double[]	calculateZeros(double start, double end, double increment, double yValue, double zValue, int recursions) Calculates a series of zeros found by the calculateZero method in the interval from the double value start to the double value end choosing guesses at every interval of the length specified by the double value increment.
double	evaluate(double x, double y, double z) Evaluates the polynomial function represented by this Polynomial object for the specified values.
Vector	evaluateGradient(double x, double y, double z) Evaluates the gradient of the polynomial funtion represented by this Polynomial object for the specified values.
Polynomial	expand(int power) Multiplies this Polynomial object with itself as many times as indicated by the specified integer value.
Polynomial	getDx() Returns a Polynomial object that represents the partial derivative of the polynomial function represented by this Polynomial object with respect to X.
Polynomial	getDy() Returns a Polynomial object that represents the partial derivative of the polynomial function represented by this Polynomial object with respect to Y.
Polynomial	getDz() Returns a Polynomial object that represents the partial derivative of the polynomial function represented by this Polynomial object with respect to Z.
Vector	getNormalAt(Vector point) Returns a Vector object that represents the vector normal to this polynomial surface at the point represented by the specified Vector object.
PolynomialTerm[]	getTerms() Returns the terms of this Polynomial object as an array of PolynomialTerm objects.
boolean	intersect(Ray ray) Returns true if the ray represented by the specified Ray object intersects the polynomial surface represented by this Polynomial object in real space.
Intersection	intersectAt(Ray ray) Returns an array of double values representing the distance along the ray represented by the specified Ray object that intersection between the ray and the polynomial surface represented by this Polynomial object occurs.
Polynomial	multiply(Polynomial polynomial) Calculates the product of the polynomial function represented by this Polynomial object and that of the specified Polynomial object and returns the result as a Polynomial object.
Polynomial	multiply(PolynomialTerm term) Calculates the product of the polynomial function represented by this Polynomial object and that of the specified PolynomialTerm object and returns the result as a Polynomial object.
void	removeTerm(int index) Removes the PolynomialTerm object stored at the specified index from this Polynomial object.
void	setTerms(PolynomialTerm[] terms) Sets the terms of this Polynomial object to those specified.
void	simplify() Scans this Polynomial object for like terms and combines them and calculates the terms of the new partial derivatives.
java.lang.String	toString() Returns a String representation of this Polynomial object.

Methods inherited from class threeD.raytracer.engine.AbstractSurface

addShader, addTexture, addTransform, calculateTransform, getColor, getColorAt, getLocation, getParent, getRotationCoefficients, getScaleCoefficients, getShadeBack, getShadeFront, getShaderSet, getSize, getTexture, getTextures, getTextureSet, getTransform, getTransform, getTransforms, removeTexture, removeTransform, setColor, setLocation, setParent, setRotationCoefficients, setScaleCoefficients, setShadeBack, setShadeFront, setShaders, setSize, setTexture, setTextures, setTransform, setTransforms, shade

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

Polynomial

public Polynomial()

Constructs a new Polynomial object with no terms.

Polynomial

public Polynomial(PolynomialTerm[] terms)

Constructs a new Polynomial object with the specified terms.

Method Detail

setTerms

public void setTerms(PolynomialTerm[] terms)

Sets the terms of this Polynomial object to those specified.

addTerm

public void addTerm(PolynomialTerm term)

Adds the specified PolynomialTerm object to this Polynomial object.

removeTerm

public void removeTerm(int index)

Removes the PolynomialTerm object stored at the specified index from this Polynomial object.

getTerms

public PolynomialTerm[] getTerms()

Returns the terms of this Polynomial object as an array of PolynomialTerm objects.

simplify

public void simplify()

Scans this Polynomial object for like terms and combines them and calculates the terms of the new partial derivatives.

add

public Polynomial add(Polynomial polynomial)

Combines the terms of this Polynomial object and the specified Polynomial object and returns the sum as a Polynomial object.

multiply

public Polynomial multiply(Polynomial polynomial)

Calculates the product of the polynomial function represented by this Polynomial object and that of the specified Polynomial object and returns the result as a Polynomial object.

multiply

public Polynomial multiply(PolynomialTerm term)

Calculates the product of the polynomial function represented by this Polynomial object and that of the specified PolynomialTerm object and returns the result as a Polynomial object.

expand

public Polynomial expand(int power)

Multiplies this Polynomial object with itself as many times as indicated by the specified integer value. If power is less than 0, null is returned. The polynomial is simplified after each step.

evaluate

public double evaluate(double x,
                       double y,
                       double z)

Evaluates the polynomial function represented by this Polynomial object for the specified values.

evaluateGradient

public Vector evaluateGradient(double x,
                               double y,
                               double z)

Evaluates the gradient of the polynomial funtion represented by this Polynomial object for the specified values.

calculateZeros

public double[] calculateZeros(double start,
                               double end,
                               double increment,
                               double yValue,
                               double zValue,
                               int recursions)

Calculates a series of zeros found by the calculateZero method in the interval from the double value start to the double value end choosing guesses at every interval of the length specified by the double value increment. The Y and Z values and the number of recursions must also be specified.

calculateZero

public double calculateZero(double initialValue,
                            double yValue,
                            double zValue,
                            int recursions)

Calculates an estimate for an X value that allows the polynomial function represented by this Polynomial object to equal zero when the specified Y and Z values are held constant. A recursive method is used and the number of recursions may be specified (3 or 4 usually works well).

getDx

public Polynomial getDx()

Returns a Polynomial object that represents the partial derivative of the polynomial function represented by this Polynomial object with respect to X.

getDy

public Polynomial getDy()

Returns a Polynomial object that represents the partial derivative of the polynomial function represented by this Polynomial object with respect to Y.

getDz

public Polynomial getDz()

Returns a Polynomial object that represents the partial derivative of the polynomial function represented by this Polynomial object with respect to Z.

calculateDx

public void calculateDx()

Calculates the terms of the partial derivative of the polynomial function represented by this Polynomial object with respect to X and stores the terms for later evaluatation.

calculateDy

public void calculateDy()

Calculates the terms of the partial derivative of the polynomial function represented by this Polynomial object with respect to Y and stores the terms for later evaluatation.

calculateDz

public void calculateDz()

Calculates the terms of the partial derivative of the polynomial function represented by this Polynomial object with respect to Z and stores the terms for later evaluatation.

getNormalAt

public Vector getNormalAt(Vector point)

Returns a Vector object that represents the vector normal to this polynomial surface at the point represented by the specified Vector object.

intersect

public boolean intersect(Ray ray)

Returns true if the ray represented by the specified Ray object intersects the polynomial surface represented by this Polynomial object in real space.

intersectAt

public Intersection intersectAt(Ray ray)

Returns an array of double values representing the distance along the ray represented by the specified Ray object that intersection between the ray and the polynomial surface represented by this Polynomial object occurs.

toString

public java.lang.String toString()

Returns a String representation of this Polynomial object.