我的查询是要以编程方式显示在体积较大的多维数据集(例如存储单元)中如何拟合各个给定的大小不同的非常规(但矩形)多维数据集(即盒子)。
数学部分被理解。像在线性编程/线性代数中一样，我们可以添加所有较小立方体的拟合体积，以找出最适合较大立方体的体积。
实际要求是最好在3d中以图形方式在网页上显示或允许这种拟合。如果可能的话，允许用户与配件互动，即改组立方体的放置等。
另外，由于我是专业Java开发人员，因此我会选择Java或相关语言/框架。但是，如果达到最终结果，我可以使用任何其他技术/框架/语言。
注意:重量也是一个问题(参数)。最大重量可以堆叠在任何给定的存储单元中。
而且，由于可以未经允许(盗贼)访问存储单元，因此堆叠在一个单元中的立方体的成本也受到限制。用户可能希望将具有较高成本的立方体安装在具有较高安全性的一个单元中，反之亦然。
示例:允许在给定的房间中安装许多装有家用电子设备的矩形盒子。这些盒子可能是电视，冰箱，洗衣机，洗碗机，游戏机，xbox 360s等的盒子。这些盒子的不同尺寸可以让您大致了解在适应有限体积的情况下的期望。
如果有相同的任何FOSS库/项目(甚至是非FOSS库或项目)，则欢迎指向它。
最佳答案
免责声明:好的，我知道它不能100％回答您的问题，也不是它古老的代码(可以从老式的CVS注释中得出结论)，而今天我不会再这样写了。但是，我测试了它，它仍然可以在Java 8上运行。但是，除了解决少量信息学挑战性问题外，水要从顶部到底部流过长方体的3D矩阵，具体取决于矩阵的“泄漏”程度(象征某种瑞士奶酪)，它还通过Java使用了非常简单的3D可视化3D因此，您需要安装Java 3D并将相应的库放到类路径中。
3D输出看起来像这样:
package vhs.bwinfo.cheese;
// $Id: Cuboid.java,v 1.1.2.1 2006/01/10 19:48:41 Robin Exp $
import javax.media.j3d.Appearance;
import javax.media.j3d.QuadArray;
import javax.media.j3d.Shape3D;
import javax.vecmath.Point3f;
import javax.vecmath.TexCoord2f;
import javax.vecmath.Vector3f;
public class Cuboid extends Shape3D {
private static final float POS = +0.5f;
private static final float NEG = -0.5f;
private static final Point3f[] POINTS = new Point3f[] {
new Point3f(NEG, NEG, NEG),
new Point3f(POS, NEG, NEG),
new Point3f(POS, NEG, POS),
new Point3f(NEG, NEG, POS),
new Point3f(NEG, POS, NEG),
new Point3f(POS, POS, NEG),
new Point3f(POS, POS, POS),
new Point3f(NEG, POS, POS)
};
private static final TexCoord2f[] TEX_COORDS = new TexCoord2f[] {
new TexCoord2f(0, 1),
new TexCoord2f(1, 1),
new TexCoord2f(1, 0),
new TexCoord2f(0, 0)
};
private static final int VERTEX_FORMAT =
QuadArray.COORDINATES |
QuadArray.NORMALS |
QuadArray.TEXTURE_COORDINATE_2;
public Cuboid(float scaleX, float scaleY, float scaleZ) {
Point3f[] points = new Point3f[8];
for (int i = 0; i < 8; i++)
points[i] = new Point3f(
POINTS[i].x * scaleX,
POINTS[i].y * scaleY,
POINTS[i].z * scaleZ
);
Point3f[] vertices = {
points[3], points[2], points[1], points[0], // bottom
points[4], points[5], points[6], points[7], // top
points[7], points[3], points[0], points[4], // left
points[6], points[5], points[1], points[2], // right
points[7], points[6], points[2], points[3], // front
points[5], points[4], points[0], points[1] // back
};
QuadArray geometry = new QuadArray(24, VERTEX_FORMAT);
geometry.setCoordinates(0, vertices);
for (int i = 0; i < 24; i++)
geometry.setTextureCoordinate(0, i, TEX_COORDS[i % 4]);
Vector3f normal = new Vector3f();
Vector3f v1 = new Vector3f();
Vector3f v2 = new Vector3f();
Point3f[] pts = new Point3f[4];
for (int i = 0; i < 4; i++)
pts[i] = new Point3f();
for (int face = 0; face < 6; face++) {
geometry.getCoordinates(face * 4, pts);
v1.sub(pts[0], pts[2]);
v2.sub(pts[1], pts[3]);
normal.cross(v1, v2);
normal.normalize();
for (int i = 0; i < 4; i++)
geometry.setNormal((face * 4 + i), normal);
}
setGeometry(geometry);
setAppearance(new Appearance());
}
public Cuboid(float scaleFactor) {
this(scaleFactor, scaleFactor, scaleFactor);
}
}
package vhs.bwinfo.cheese;
// $Id: LeakyCheese.java,v 1.2.2.2 2006/01/10 15:37:14 Robin Exp $
import com.sun.j3d.utils.applet.JMainFrame;
import javax.swing.*;
import java.util.Random;
import static java.lang.System.out;
public class LeakyCheese {
private int width = 20, height = 20, depth = 20;
private int numClasses = 100, samplesPerClass = 100;
private double pMin = 0, pMax = 1;
private double pDiff = pMax - pMin;
private double classSize = pDiff / numClasses;
private int[] stats;
enum CubeState {CHEESE, AIR, WATER}
final private CubeState[][][] cheese;
private static final Random RND = new Random();
public LeakyCheese(
int width, int height, int depth,
int numClasses, int samplesPerClass,
double pMin, double pMax
) {
this.width = width;
this.height = height;
this.depth = depth;
this.numClasses = numClasses;
this.samplesPerClass = samplesPerClass;
this.pMin = pMin;
this.pMax = pMax;
pDiff = pMax - pMin;
classSize = pDiff / numClasses;
cheese = new CubeState[width][height][depth];
}
public LeakyCheese(
int width, int height, int depth,
int numClasses, int samplesPerClass
) {
this(width, height, depth, numClasses, samplesPerClass, 0, 1);
}
public LeakyCheese() {
cheese = new CubeState[width][height][depth];
}
private boolean pourWater(int x, int y, int z) {
if (x < 0 || x >= width || y < 0 || y >= height || z < 0 || z >= depth)
return false;
if (cheese[x][y][z] != CubeState.AIR)
return false;
cheese[x][y][z] = CubeState.WATER;
boolean retVal = (y == 0);
retVal = pourWater(x + 1, y, z) || retVal;
retVal = pourWater(x - 1, y, z) || retVal;
retVal = pourWater(x, y + 1, z) || retVal;
retVal = pourWater(x, y - 1, z) || retVal;
retVal = pourWater(x, y, z + 1) || retVal;
retVal = pourWater(x, y, z - 1) || retVal;
return retVal;
}
private boolean isLeaky(double p) {
for (int x = 0; x < width; x++)
for (int y = 0; y < height; y++)
for (int z = 0; z < depth; z++)
cheese[x][y][z] = (RND.nextDouble() < p)
? CubeState.CHEESE
: CubeState.AIR;
boolean retVal = false;
for (int x = 0; x < width; x++)
for (int z = 0; z < depth; z++)
retVal = pourWater(x, height - 1, z) || retVal;
return retVal;
}
private void generateStats() {
if (stats != null)
return;
stats = new int[numClasses];
for (int i = 0; i < numClasses; i++) {
for (int j = 0; j < samplesPerClass; j++) {
double p = pMin + classSize * (RND.nextDouble() + i);
if (isLeaky(p))
stats[i]++;
}
}
}
public void printStats() {
generateStats();
out.println(
"p (cheese) | p (leaky)\n" +
"------------------+-----------"
);
for (int i = 0; i < numClasses; i++) {
out.println(
String.format(
"%1.5f..%1.5f | %1.5f",
pMin + classSize * i,
pMin + classSize * (i + 1),
(double) stats[i] / samplesPerClass
)
);
}
}
public static void main(String[] args) {
//new LeakyCheese().printStats();
//new LeakyCheese(40, 40, 40, 50, 100, 0.66, .71).printStats();
LeakyCheese cheeseBlock = new LeakyCheese(5, 20, 5, 20, 100);
//LeakyCheese cheeseBlock = new LeakyCheese(20, 20, 20, 20, 100);
while (!cheeseBlock.isLeaky(0.65))
;
out.println("*** required solution found - now rendering... ***");
JMainFrame f = new JMainFrame(new LeakyCheeseGUI(cheeseBlock.cheese), 512, 512);
f.setLocationRelativeTo(null);
f.setExtendedState(JFrame.MAXIMIZED_BOTH);
}
}
package vhs.bwinfo.cheese;
// $Id: LeakyCheeseGUI.java,v 1.1.2.1 2006/01/10 15:25:18 Robin Exp $
import com.sun.j3d.utils.applet.MainFrame;
import com.sun.j3d.utils.universe.SimpleUniverse;
import vhs.bwinfo.cheese.LeakyCheese.CubeState;
import javax.media.j3d.*;
import javax.vecmath.Point3d;
import javax.vecmath.Vector3f;
import java.applet.Applet;
import java.awt.*;
import java.util.Random;
public class LeakyCheeseGUI extends Applet {
static final long serialVersionUID = -8194627556699837928L;
public BranchGroup createSceneGraph(CubeState[][][] cheese) {
// Create the root of the branch graph
BranchGroup bgRoot = new BranchGroup();
// Composite of two rotations around different axes. The resulting
// TransformGroup is the parent of all our cheese cubes, because their
// orientation is identical. They only differ in their translation
// values and colours.
Transform3D tRotate = new Transform3D();
Transform3D tRotateTemp = new Transform3D();
tRotate.rotX(Math.PI / 8.0d);
tRotateTemp.rotY(Math.PI / -4.0d);
tRotate.mul(tRotateTemp);
TransformGroup tgRotate = new TransformGroup(tRotate);
bgRoot.addChild(tgRotate);
// Bounding sphere for rendering
BoundingSphere bounds =
new BoundingSphere(new Point3d(0.0, 0.0, 0.0), 100.0);
// Set background colour
// Note: Using Canvas3D.setBackground does not work, because it is an
// AWT method. Java 3D, though, gets its background colour from its
// background node (black, if not present).
Background background = new Background(0.5f, 0.5f, 0.5f);
background.setApplicationBounds(bounds);
bgRoot.addChild(background);
TransparencyAttributes transpAttr;
// Little cheese cubes
Appearance cheeseAppearance = new Appearance();
transpAttr =
new TransparencyAttributes(TransparencyAttributes.NICEST, 0.98f);
cheeseAppearance.setTransparencyAttributes(transpAttr);
cheeseAppearance.setColoringAttributes(
new ColoringAttributes(1, 1, 0, ColoringAttributes.NICEST));
PolygonAttributes pa = new PolygonAttributes();
//pa.setPolygonMode(PolygonAttributes.POLYGON_LINE);
pa.setCullFace(PolygonAttributes.CULL_NONE);
cheeseAppearance.setPolygonAttributes(pa);
// Little water cubes
Appearance waterAppearance = new Appearance();
transpAttr =
new TransparencyAttributes(TransparencyAttributes.NICEST, 0.85f);
waterAppearance.setTransparencyAttributes(transpAttr);
waterAppearance.setColoringAttributes(
new ColoringAttributes(0, 0, 1, ColoringAttributes.NICEST));
pa = new PolygonAttributes();
pa.setCullFace(PolygonAttributes.CULL_NONE);
waterAppearance.setPolygonAttributes(pa);
// Little air cubes
Appearance airAppearance = new Appearance();
transpAttr =
new TransparencyAttributes(TransparencyAttributes.NICEST, 0.95f);
airAppearance.setTransparencyAttributes(transpAttr);
airAppearance.setColoringAttributes(
new ColoringAttributes(1, 1, 1, ColoringAttributes.NICEST));
pa = new PolygonAttributes();
//pa.setPolygonMode(PolygonAttributes.POLYGON_LINE);
pa.setCullFace(PolygonAttributes.CULL_NONE);
airAppearance.setPolygonAttributes(pa);
// Water-coloured (i.e. blue) wire frame around cheese block, if leaky
Appearance waterWireFrameAppearance = new Appearance();
waterWireFrameAppearance.setColoringAttributes(
new ColoringAttributes(0, 0, 1, ColoringAttributes.NICEST));
pa = new PolygonAttributes();
pa.setPolygonMode(PolygonAttributes.POLYGON_LINE);
pa.setCullFace(PolygonAttributes.CULL_NONE);
waterWireFrameAppearance.setPolygonAttributes(pa);
// Cheese-coloured (i.e. yellow) wire frame around cheese block, if not leaky
Appearance cheeseWireFrameAppearance = new Appearance();
cheeseWireFrameAppearance.setColoringAttributes(
new ColoringAttributes(1, 1, 0, ColoringAttributes.NICEST));
pa = new PolygonAttributes();
pa.setPolygonMode(PolygonAttributes.POLYGON_LINE);
pa.setCullFace(PolygonAttributes.CULL_NONE);
cheeseWireFrameAppearance.setPolygonAttributes(pa);
// Absolute offsets for the cheese block to fit into the viewing canvas
final float xOffs = -0.8f;
final float yOffs = -0.55f;
final float zOffs = 0;
// Create all those little cubes ;-)
final int xSize = cheese.length;
final int ySize = cheese[0].length;
final int zSize = cheese[0][0].length;
final int maxSize = Math.max(xSize, Math.max(ySize, zSize));
final float xCenterOffs = 0.5f * (maxSize - xSize) / maxSize;
final float yCenterOffs = 0.5f * (maxSize - ySize) / maxSize;
final float zCenterOffs = -0.5f * (maxSize - zSize) / maxSize;
boolean isLeaky = false;
for (int x = 0; x < xSize; x++)
for (int y = 0; y < ySize; y++)
for (int z = 0; z < zSize; z++) {
Transform3D tTranslate = new Transform3D();
tTranslate.setTranslation(
new Vector3f(
xOffs + xCenterOffs + 1.0f * x / maxSize,
yOffs + yCenterOffs + 1.0f * y / maxSize,
zOffs + zCenterOffs - 1.0f * z / maxSize
)
);
TransformGroup tgTranslate = new TransformGroup(tTranslate);
tgRotate.addChild(tgTranslate);
Cuboid cube = new Cuboid(1.0f / maxSize);
switch (cheese[x][y][z]) {
case CHEESE:
cube.setAppearance(cheeseAppearance);
break;
case WATER:
cube.setAppearance(waterAppearance);
if (y == 0)
isLeaky = true;
break;
case AIR:
cube.setAppearance(airAppearance);
}
tgTranslate.addChild(cube);
}
// If cheese block is leaky, visualise it by drawing a water-coloured
// (i.e. blue) wire frame around it. Otherwise use a cheese-coloured
// (i.e. yellow) one.
Transform3D tTranslate = new Transform3D();
tTranslate.setTranslation(
new Vector3f(
xOffs + xCenterOffs + 0.5f * (xSize - 1) / maxSize,
yOffs + yCenterOffs + 0.5f * (ySize - 1) / maxSize,
zOffs + zCenterOffs - 0.5f * (zSize - 1) / maxSize
)
);
TransformGroup tgTranslate = new TransformGroup(tTranslate);
tgRotate.addChild(tgTranslate);
Cuboid cuboid = new Cuboid(
1.0f * xSize / maxSize,
1.0f * ySize / maxSize,
1.0f * zSize / maxSize
);
cuboid.setAppearance(isLeaky ? waterWireFrameAppearance : cheeseWireFrameAppearance);
tgTranslate.addChild(cuboid);
// Let Java 3D perform optimizations on this scene graph.
bgRoot.compile();
return bgRoot;
}
public LeakyCheeseGUI(CubeState[][][] cheese) {
// Create a simple scene and attach it to the virtual universe
GraphicsConfiguration graphCfg = SimpleUniverse.getPreferredConfiguration();
Canvas3D canvas = new Canvas3D(graphCfg);
setLayout(new BorderLayout());
add(canvas, "Center");
SimpleUniverse universe = new SimpleUniverse(canvas);
// This will move the ViewPlatform back a bit so the objects
// in the scene can be viewed.
universe.getViewingPlatform().setNominalViewingTransform();
universe.addBranchGraph(createSceneGraph(cheese));
}
public static void main(String[] args) {
final Random RND = new Random(System.currentTimeMillis());
CubeState[][][] testCheese = new CubeState[5][8][11];
for (int x = 0; x < 5; x++)
for (int y = 0; y < 8; y++)
for (int z = 0; z < 11; z++)
testCheese[x][y][z] = (RND.nextFloat() < 0.7f)
? CubeState.CHEESE
: (RND.nextBoolean() ? CubeState.WATER : CubeState.AIR);
// Applet can also run as a stand-alone application
new MainFrame(new LeakyCheeseGUI(testCheese), 512, 512);
}
}