java - 将矩阵(二维数组)旋转 X.XX°

Question

我无法找到有关以下主题的任何内容，因为大多数问题都要求将阵列旋转 90°、180°、270°，这实际上很容易。

我需要将矩阵转换为所有可能的度数，就像我在 Photoshop 中旋转图像一样(以编程方式，我不需要 GUI 或类似的东西)。这会导致结果出现一些小错误，但不会造成太大影响。

图片旋转应该是一个非常相似的方法，所以我认为这个问题应该有很多解决方案。 java中有没有一种简单的方法可以做到这一点，或者我必须自己计算每个条目的位置？

注意:我使用的数组是一个“二进制”数组，填充了值为“0”和“1”的整数。

PS:这将改变矩阵周围“边界框”的大小。此时这没有问题。

<小时/>

编辑:我尝试举一个例子:

初始:

{ 0, 0, 1, 0 }
{ 0, 0, 1, 0 }
{ 0, 0, 1, 0 }
{ 0, 0, 1, 0 }
{ 0, 0, 1, 0 }
{ 0, 0, 1, 0 }

在旋转点[3][2]处旋转20.12°。

结果:

{ 0, 0, 0, 1 }
{ 0, 0, 1, 0 }
{ 0, 0, 1, 0 }
{ 0, 0, 1, 0 }
{ 0, 0, 1, 0 }
{ 0, 1, 0, 0 }

这看起来非常无用，但是这个矩阵的大小越大，结果就越准确。我使用的矩阵比这个例子大得多。 :)

Answer 1

我会编写两种方法:一种将数组转换为 BufferedImage，另一种则相反。这两件事都应该很容易实现。 BufferedImage可以通过AffineTransform等进行旋转
不是很优雅，但可以在没有第三方东西的情况下使用标准 java 代码。
您将获得以图形方式显示结果的图像。

此实现执行上述操作:

package rasterImage;

import java.awt.Graphics2D;
import java.awt.geom.AffineTransform;
import java.awt.image.BufferedImage;

public class MatrixRotator extends javax.swing.JFrame {

    public MatrixRotator() {
        initComponents();
        setLocationRelativeTo(null);
    }

    @SuppressWarnings("unchecked")
    // <editor-fold defaultstate="collapsed" desc="Generated Code">                          
    private void initComponents() {

        jButtonDoIt = new javax.swing.JButton();
        jPanelOrg = new javax.swing.JPanel();
        jPanelRot = new javax.swing.JPanel();

        setDefaultCloseOperation(javax.swing.WindowConstants.EXIT_ON_CLOSE);

        jButtonDoIt.setText("Do it");
        jButtonDoIt.addActionListener(new java.awt.event.ActionListener() {
            public void actionPerformed(java.awt.event.ActionEvent evt) {
                jButtonDoItActionPerformed(evt);
            }
        });

        jPanelOrg.setBorder(javax.swing.BorderFactory.createLineBorder(new java.awt.Color(0, 0, 0)));

        javax.swing.GroupLayout jPanelOrgLayout = new javax.swing.GroupLayout(jPanelOrg);
        jPanelOrg.setLayout(jPanelOrgLayout);
        jPanelOrgLayout.setHorizontalGroup(
            jPanelOrgLayout.createParallelGroup(javax.swing.GroupLayout.Alignment.LEADING)
            .addGap(0, 100, Short.MAX_VALUE)
        );
        jPanelOrgLayout.setVerticalGroup(
            jPanelOrgLayout.createParallelGroup(javax.swing.GroupLayout.Alignment.LEADING)
            .addGap(0, 100, Short.MAX_VALUE)
        );

        jPanelRot.setBorder(javax.swing.BorderFactory.createLineBorder(new java.awt.Color(0, 0, 0)));

        javax.swing.GroupLayout jPanelRotLayout = new javax.swing.GroupLayout(jPanelRot);
        jPanelRot.setLayout(jPanelRotLayout);
        jPanelRotLayout.setHorizontalGroup(
            jPanelRotLayout.createParallelGroup(javax.swing.GroupLayout.Alignment.LEADING)
            .addGap(0, 100, Short.MAX_VALUE)
        );
        jPanelRotLayout.setVerticalGroup(
            jPanelRotLayout.createParallelGroup(javax.swing.GroupLayout.Alignment.LEADING)
            .addGap(0, 100, Short.MAX_VALUE)
        );

        javax.swing.GroupLayout layout = new javax.swing.GroupLayout(getContentPane());
        getContentPane().setLayout(layout);
        layout.setHorizontalGroup(
            layout.createParallelGroup(javax.swing.GroupLayout.Alignment.LEADING)
            .addGroup(layout.createSequentialGroup()
                .addContainerGap()
                .addGroup(layout.createParallelGroup(javax.swing.GroupLayout.Alignment.LEADING)
                    .addComponent(jButtonDoIt)
                    .addGroup(layout.createSequentialGroup()
                        .addComponent(jPanelOrg, javax.swing.GroupLayout.PREFERRED_SIZE, javax.swing.GroupLayout.DEFAULT_SIZE, javax.swing.GroupLayout.PREFERRED_SIZE)
                        .addPreferredGap(javax.swing.LayoutStyle.ComponentPlacement.UNRELATED)
                        .addComponent(jPanelRot, javax.swing.GroupLayout.PREFERRED_SIZE, javax.swing.GroupLayout.DEFAULT_SIZE, javax.swing.GroupLayout.PREFERRED_SIZE)))
                .addContainerGap(javax.swing.GroupLayout.DEFAULT_SIZE, Short.MAX_VALUE))
        );
        layout.setVerticalGroup(
            layout.createParallelGroup(javax.swing.GroupLayout.Alignment.LEADING)
            .addGroup(layout.createSequentialGroup()
                .addContainerGap()
                .addGroup(layout.createParallelGroup(javax.swing.GroupLayout.Alignment.TRAILING)
                    .addComponent(jPanelRot, javax.swing.GroupLayout.PREFERRED_SIZE, javax.swing.GroupLayout.DEFAULT_SIZE, javax.swing.GroupLayout.PREFERRED_SIZE)
                    .addGroup(layout.createSequentialGroup()
                        .addComponent(jButtonDoIt)
                        .addPreferredGap(javax.swing.LayoutStyle.ComponentPlacement.UNRELATED)
                        .addComponent(jPanelOrg, javax.swing.GroupLayout.PREFERRED_SIZE, javax.swing.GroupLayout.DEFAULT_SIZE, javax.swing.GroupLayout.PREFERRED_SIZE)))
                .addContainerGap(javax.swing.GroupLayout.DEFAULT_SIZE, Short.MAX_VALUE))
        );

        pack();
    }// </editor-fold>                        

    private void printRaster(int[][] raster) {
        int rows = raster.length;
        int cols = raster[0].length;

        for (int r = 0; r < rows; r++) {
            for (int c = 0; c < cols; c++) {
                int content = raster[r][c];
                System.out.print(content);
            }
            System.out.println();
        }
    }

    private BufferedImage convert2image(int[][] raster) {
        int rows = raster.length;
        int cols = raster[0].length;

        BufferedImage img = new BufferedImage(cols, rows, BufferedImage.TYPE_BYTE_BINARY);
        Graphics2D g = img.createGraphics();

        for (int r = 0; r < rows; r++) {
            for (int c = 0; c < cols; c++) {
                int content = raster[r][c];
                if (content == 1) {
                    g.fillRect(c, r, 1, 1);
                }
            }
        }

        return img;
    }

    private int[][] convert2raster(BufferedImage img) {
        int cols = img.getWidth();
        int rows = img.getHeight();
        int[][] raster = new int[rows][cols];

        for (int r = 0; r < rows; r++) {
            for (int c = 0; c < cols; c++) {
                int content = img.getRGB(c, r);
                if (content == -1) {
                    raster[r][c] = 1;
                } else {
                    raster[r][c] = 0;
                }
            }
        }

        return raster;
    }

    private void jButtonDoItActionPerformed(java.awt.event.ActionEvent evt) {                                            
        int[][] raster = {{0, 0, 1, 0}, {0, 0, 1, 0}, {0, 0, 1, 0}, {0, 0, 1, 0}, {0, 0, 1, 0}, {0, 0, 1, 0}};
        printRaster(raster);

        //convert raster to image:
        BufferedImage img = convert2image(raster);

        //create rotated image ('large enough'):
        BufferedImage imgRot = new BufferedImage(10, 10, BufferedImage.TYPE_BYTE_BINARY);

        //rotate the image:
        AffineTransform tx = new AffineTransform();
        tx.rotate(Math.toRadians(20.12));
        imgRot.createGraphics().drawImage(img, tx, null);

        //convert image to raster:
        raster = convert2raster(imgRot);
        printRaster(raster);

        //draw it:
        jPanelOrg.getGraphics().drawImage(img, 0, 0, null);
        jPanelRot.getGraphics().drawImage(imgRot, 0, 0, null);
    }                                           

    public static void main(String args[]) {
        java.awt.EventQueue.invokeLater(new Runnable() {
            @Override
            public void run() {
                new MatrixRotator().setVisible(true);
            }
        });
    }

    // Variables declaration - do not modify                     
    private javax.swing.JButton jButtonDoIt;
    private javax.swing.JPanel jPanelOrg;
    private javax.swing.JPanel jPanelRot;
    // End of variables declaration                   
}