261 lines
12 KiB
Java
261 lines
12 KiB
Java
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import java.awt.*;
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import java.awt.geom.*;
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import java.awt.image.*;
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/**
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* This class is for defining triangulated images and for interpolation
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* between two triangulated images with corresponding triangulations.
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*
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* @author Frank Klawonn
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* Last change 31.05.2005
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*
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* @see MorphingCandS
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*/
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public class TriangulatedImage
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{
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//The initial image.
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BufferedImage bi;
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//The points needed for the triangulation.
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Point2D[] tPoints;
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//The triangles defining the triangulation. Each row of the arrays contains
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//indices of three points in the array tPoints. The i-th triangle of the
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//triangulation is defined by the three points in array tPoints with the indices
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//triangles[i][0], triangles[i][1], triangles[i][2].
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int[][] triangles;
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/**
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* A method that computes for a point v and three additional noncollinear points
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* a representation of v as a linear combination of the three points. The three coefficents
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* for the representation of v are returned.
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*
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* @param v point to be represented.
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* @param triangle an array contain three noncollinear points.
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*
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* @return the three coefficients for the representation of v.
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*/
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public static double[] triangleCoordinates(Point2D v, Point2D[] triangle)
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{
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//The array for the three coefficients.
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double[] result = new double[3];
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//Some values that are needed to solve the system of linear equations for
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//determining the coefficients.
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double d13x = triangle[0].getX() - triangle[2].getX();
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double d23x = triangle[1].getX() - triangle[2].getX();
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double dx3 = v.getX() - triangle[2].getX();
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double d13y = triangle[0].getY() - triangle[2].getY();
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double d23y = triangle[1].getY() - triangle[2].getY();
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double dy3 = v.getY() - triangle[2].getY();
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double delta = d13x*d23y - d23x*d13y;
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//When the three points are (almost) collinear, division by zero is avoided and
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//coefficients are returned which at least do not represent a convex combinaion.
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//Otherwise the coefficients cannot be computed.
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if (Math.abs(delta)<0.00000001)
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{
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result[0] = 10;
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}
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else
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{
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result[0] = (dx3*d23y - d23x*dy3)/delta;
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result[1] = (d13x*dy3 - dx3*d13y)/delta;
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}
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result[2] = 1 - result[0] - result[1];
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return(result);
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}
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/**
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* Test, whether a given array of coefficienten represents a convex combination,
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* i.e. it is checked, whether all elements in the array are between 0 and 1
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* and whether they sum up to 1.
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*
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* @param t array with the coefficients.
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*
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* @return true if and only if the coefficients represent a convex combination.
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*/
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public static boolean isConvexCombination(double[] t)
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{
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boolean result;
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double sum;
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//According to round-off errors, the coefficients will almost never sum up to 1 exactly.
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//The following value specifies how much deviation from the exact value 1 is still considered
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//as a convex combination.
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double tolerance = 0.000001;
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result = true;
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sum = 0;
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for (int i=0; i<t.length; i++)
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{
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if (t[i]<0 || t[i]>1)
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{
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result = false;
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}
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sum = sum + t[i];
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}
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if (Math.abs(sum-1)>tolerance)
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{
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result = false;
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}
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return(result);
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}
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/**
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* Generates and interpolated image from two triangulated images (this and ti).
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* ti contribued to the interpolated image by alpha*100%. The two images must have the
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* same size, the same number of points for the triangulation and the number of triangles.
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* Furthermore, the triangles for both images must consist of the points with the same
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* indices. Only the position of the points does need to coincide for the two images.
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*
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* @param ti second triangulated image.
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* @param alpha proportion that ti should contribute to the interpolated image.
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*
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* @return the interpolated image.
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*/
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public BufferedImage mixWith(TriangulatedImage ti, double alpha)
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{
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TriangulatedImage mix = new TriangulatedImage();
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//Here the interpolated image will be stored.
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mix.bi = new BufferedImage(this.bi.getWidth(),this.bi.getHeight(),
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BufferedImage.TYPE_INT_RGB);
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//Define the points for the triangulation points in the interpolated image as
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//convex combinations of the corresponding points in the images to be
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//interpolated.
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mix.tPoints = new Point2D[this.tPoints.length];
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for (int i=0; i<mix.tPoints.length; i++)
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{
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mix.tPoints[i] = new Point2D.Double((1-alpha)*this.tPoints[i].getX()
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+ alpha*ti.tPoints[i].getX(),
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(1-alpha)*this.tPoints[i].getY()
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+ alpha*ti.tPoints[i].getY());
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}
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//The triangles for the triangulation must be defined using the same points (indices)
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//as in the original images.
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mix.triangles = this.triangles;
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int rgbValueThis;
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int rgbValueTi;
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int rgbValueMix;
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Color thisColour;
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Color tiColour;
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Color pixelColour;
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int rMix;
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int gMix;
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int bMix;
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int xInt;
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int yInt;
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double[] t = new double[3];
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double aux;
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Point2D[] threePoints = new Point2D[3];;
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Point2D.Double pixel = new Point2D.Double();
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int tNo;
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boolean notFound;
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//Determine for each pixel in the interpolated image the colour as a
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//convex combination of the RGB-values of the corresponding pixels in the
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//two images to be interpolated.
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for (int i=0; i<mix.bi.getWidth(); i++)
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{
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for (int j=0; j<mix.bi.getHeight(); j++)
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{
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//For this pixel the colour must be determined.
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pixel.setLocation(i,j);
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//tNo is used to compute the index of the triangle in which the
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//considered pixel lies.
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tNo = 0;
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//When the triangle has been found, notFound changes to false.
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notFound = true;
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while(tNo<mix.triangles.length && notFound)
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{
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//Determine the three points of the triangle no. tNo.
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for(int k=0; k<3; k++)
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{
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threePoints[k] = mix.tPoints[mix.triangles[tNo][k]];
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}
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//Determine the coordinates of the pixels w.r.t. to the triangle no. tNo.
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t = triangleCoordinates(pixel,threePoints);
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//Check whether the pixel lies inside the triangle.
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if (isConvexCombination(t))
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{
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notFound = false;
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}
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else
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{
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tNo++;
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}
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}//endWhile
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//The while-loop terminates when an index tNo of a triangle containing the
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//pixel has been found or when no triangle containing the pixel has been found.
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//If a triangle containing the pixel has been found, the colour for the pixel
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//can be computed.
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if (!notFound)
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{
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//Determine the x-coordinate of the pixel in the first image (this) as
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//a convex combination of the vertices of the corresponding triangle.
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aux = 0;
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for (int k=0; k<3; k++)
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{
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aux = aux + t[k]*this.tPoints[this.triangles[tNo][k]].getX();
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}
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xInt = (int) Math.round(aux);
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//We have to make sure that round-off errors will not lead to a pixel
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//outside the image.
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xInt = Math.max(0,xInt);
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xInt = Math.min(this.bi.getWidth()-1,xInt);
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//The same for the y-coordinate.
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aux = 0;
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for (int k=0; k<3; k++)
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{
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aux = aux + t[k]*this.tPoints[this.triangles[tNo][k]].getY();
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}
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yInt = (int) Math.round(aux);
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yInt = Math.max(0,yInt);
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yInt = Math.min(this.bi.getHeight()-1,yInt);
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//Determine the colour of the pixel in the first image.
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rgbValueThis = this.bi.getRGB(xInt,yInt);
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thisColour = new Color(rgbValueThis);
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//Do the same as above for the second image ti.
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aux = 0;
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for (int k=0; k<3; k++)
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{
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aux = aux + t[k]*ti.tPoints[ti.triangles[tNo][k]].getX();
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}
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xInt = (int) Math.round(aux);
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aux = 0;
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for (int k=0; k<3; k++)
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{
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aux = aux + t[k]*ti.tPoints[ti.triangles[tNo][k]].getY();
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}
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yInt = (int) Math.round(aux);
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rgbValueTi = ti.bi.getRGB(xInt,yInt);
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tiColour = new Color(rgbValueTi);
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//Now that we have the two colours, we can compute their
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//convex combimation for the R-,G- and B-value.
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//Problems caused by round-off errors are quite unlikely here.
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rMix = (int) Math.round((1-alpha)*thisColour.getRed()+
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alpha*tiColour.getRed());
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gMix = (int) Math.round((1-alpha)*thisColour.getGreen()+
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alpha*tiColour.getGreen());
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bMix = (int) Math.round((1-alpha)*thisColour.getBlue()+
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alpha*tiColour.getBlue());
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//Generate the interpolated colour as a convex combination.
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pixelColour = new Color(rMix, gMix, bMix);
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//Use the interpolated colour to draw the pixel in the interpolated image
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mix.bi.setRGB(i,j,pixelColour.getRGB());
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}//endif (!notFound)
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}//endfor j
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}//endfor i
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return(mix.bi);
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}
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}
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