package de.lmu.ifi.dbs.elki.visualization.projections;
/*
This file is part of ELKI:
Environment for Developing KDD-Applications Supported by Index-Structures
Copyright (C) 2011
Ludwig-Maximilians-Universität München
Lehr- und Forschungseinheit für Datenbanksysteme
ELKI Development Team
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU Affero General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Affero General Public License for more details.
You should have received a copy of the GNU Affero General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
import java.util.BitSet;
import de.lmu.ifi.dbs.elki.data.NumberVector;
import de.lmu.ifi.dbs.elki.math.DoubleMinMax;
import de.lmu.ifi.dbs.elki.math.linearalgebra.AffineTransformation;
import de.lmu.ifi.dbs.elki.math.linearalgebra.Vector;
import de.lmu.ifi.dbs.elki.utilities.pairs.Pair;
import de.lmu.ifi.dbs.elki.visualization.scales.LinearScale;
import de.lmu.ifi.dbs.elki.visualization.svg.SVGUtil;
/**
* Affine projections are the most general class. They are initialized by an
* arbitrary affine transformation matrix, and can thus represent any rotation
* and scaling, even simple perspective projections.
*
* However, this comes at the cost of a matrix multiplication.
*
* @author Erich Schubert
*/
public class AffineProjection extends AbstractProjection implements Projection2D {
/**
* Affine transformation used in projection
*/
private AffineTransformation proj;
/**
* Constructor with a given database and axes.
*
* @param scales Scales to use
* @param proj Projection to use
*/
public AffineProjection(LinearScale[] scales, AffineTransformation proj) {
super(scales);
this.proj = proj;
}
/**
* Project a vector from scaled space to rendering space.
*
* @param v vector in scaled space
* @return vector in rendering space
*/
@Override
public Vector projectScaledToRender(Vector v) {
return proj.apply(v);
}
/**
* Project a vector from rendering space to scaled space.
*
* @param v vector in rendering space
* @return vector in scaled space
*/
@Override
public Vector projectRenderToScaled(Vector v) {
return proj.applyInverse(v);
}
/**
* Project a relative vector from scaled space to rendering space.
*
* @param v relative vector in scaled space
* @return relative vector in rendering space
*/
@Override
public Vector projectRelativeScaledToRender(Vector v) {
return proj.applyRelative(v);
}
/**
* Project a relative vector from rendering space to scaled space.
*
* @param v relative vector in rendering space
* @return relative vector in scaled space
*/
@Override
public Vector projectRelativeRenderToScaled(Vector v) {
return proj.applyRelativeInverse(v);
}
@Override
public Pair<DoubleMinMax, DoubleMinMax> estimateViewport() {
final int dim = proj.getDimensionality();
DoubleMinMax minmaxx = new DoubleMinMax();
DoubleMinMax minmaxy = new DoubleMinMax();
// Origin
Vector orig = new Vector(dim);
orig = projectScaledToRender(orig);
minmaxx.put(orig.get(0));
minmaxy.put(orig.get(1));
// Diagonal point
Vector diag = new Vector(dim);
for(int d2 = 0; d2 < dim; d2++) {
diag.set(d2, 1);
}
diag = projectScaledToRender(diag);
minmaxx.put(diag.get(0));
minmaxy.put(diag.get(1));
// Axis end points
for(int d = 0; d < dim; d++) {
Vector v = new Vector(dim);
v.set(d, 1);
Vector ax = projectScaledToRender(v);
minmaxx.put(ax.get(0));
minmaxy.put(ax.get(1));
}
return new Pair<DoubleMinMax, DoubleMinMax>(minmaxx, minmaxy);
}
@Override
public String estimateTransformString(double margin, double width, double height) {
Pair<DoubleMinMax, DoubleMinMax> minmax = estimateViewport();
double sizex = (minmax.first.getMax() - minmax.first.getMin());
double sizey = (minmax.second.getMax() - minmax.second.getMin());
return SVGUtil.makeMarginTransform(width, height, sizex, sizey, margin) + " translate(" + SVGUtil.fmt(sizex / 2) + " " + SVGUtil.fmt(sizey / 2) + ")";
}
/**
* Compute an transformation matrix to show only axis ax1 and ax2.
*
* @param dim Dimensionality
* @param ax1 First axis
* @param ax2 Second axis
* @return transformation matrix
*/
public static AffineTransformation axisProjection(int dim, int ax1, int ax2) {
// setup a projection to get the data into the interval -1:+1 in each
// dimension with the intended-to-see dimensions first.
AffineTransformation proj = AffineTransformation.reorderAxesTransformation(dim, new int[] { ax1, ax2 });
// Assuming that the data was normalized on [0:1], center it:
double[] trans = new double[dim];
for(int i = 0; i < dim; i++) {
trans[i] = -.5;
}
proj.addTranslation(new Vector(trans));
// mirror on the y axis, since the SVG coordinate system is screen
// coordinates (y = down) and not mathematical coordinates (y = up)
proj.addAxisReflection(2);
// scale it up
proj.addScaling(SCALE);
return proj;
}
@Override
public double[] fastProjectDataToRenderSpace(Vector data) {
return fastProjectScaledToRender(projectDataToScaledSpace(data));
}
@Override
public double[] fastProjectDataToRenderSpace(NumberVector<?, ?> data) {
return fastProjectScaledToRender(projectDataToScaledSpace(data));
}
@Override
public double[] fastProjectScaledToRender(Vector v) {
final double[] vr = v.getArrayRef();
double x = 0.0;
double y = 0.0;
double s = 0.0;
final double[][] matrix = proj.getTransformation().getArrayRef();
final double[] colx = matrix[0];
final double[] coly = matrix[1];
final double[] cols = matrix[vr.length];
assert (colx.length == coly.length && colx.length == cols.length && cols.length == vr.length + 1);
for(int k = 0; k < vr.length; k++) {
x += colx[k] * vr[k];
y += coly[k] * vr[k];
s += cols[k] * vr[k];
}
// add homogene component:
x += colx[vr.length];
y += coly[vr.length];
s += cols[vr.length];
assert (s != 0.0);
return new double[] { x / s, y / s };
}
@Override
public double[] fastProjectRelativeDataToRenderSpace(Vector data) {
return fastProjectRelativeScaledToRender(projectRelativeDataToScaledSpace(data));
}
@Override
public double[] fastProjectRelativeDataToRenderSpace(NumberVector<?, ?> data) {
return fastProjectRelativeScaledToRender(projectRelativeDataToScaledSpace(data));
}
@Override
public double[] fastProjectRelativeScaledToRender(Vector v) {
final double[] vr = v.getArrayRef();
double x = 0.0;
double y = 0.0;
final double[][] matrix = proj.getTransformation().getArrayRef();
final double[] colx = matrix[0];
final double[] coly = matrix[1];
assert (colx.length == coly.length);
for(int k = 0; k < vr.length; k++) {
x += colx[k] * vr[k];
y += coly[k] * vr[k];
}
return new double[] { x, y };
}
@Override
public BitSet getVisibleDimensions2D() {
final int dim = proj.getDimensionality();
BitSet actDim = new BitSet(dim);
Vector vScale = new Vector(dim);
for(int d = 0; d < dim; d++) {
vScale.setZero();
vScale.set(d, 1);
double[] vRender = fastProjectScaledToRender(vScale);
// TODO: Can't we do this by inspecting the projection matrix directly?
if(vRender[0] != 0.0 || vRender[1] != 0) {
actDim.set(d);
}
}
return actDim;
}
}