Q
纹理变形,4分
3
A
回答
8
好的,我们走吧。实现为小型,独立的例子就可以在拐角处使用鼠标拖动:
+1到...
- 南美长吻海豚谁已经公布的基本办法,his answer
- MVG在math.stackexchange.com谁描述how to compute a projective transformation from 4 points
下面的代码:
import java.awt.Color;
import java.awt.Graphics;
import java.awt.GridLayout;
import java.awt.Point;
import java.awt.event.MouseEvent;
import java.awt.event.MouseListener;
import java.awt.event.MouseMotionListener;
import java.awt.geom.Point2D;
import java.awt.image.BufferedImage;
import java.io.File;
import java.io.IOException;
import javax.imageio.ImageIO;
import javax.swing.ImageIcon;
import javax.swing.JFrame;
import javax.swing.JLabel;
import javax.swing.JPanel;
import javax.swing.SwingUtilities;
public class Pseudo3DTest
{
public static void main(String[] args)
{
SwingUtilities.invokeLater(new Runnable()
{
@Override
public void run()
{
createAndShowGUI();
}
});
}
private static void createAndShowGUI()
{
JFrame f = new JFrame();
f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
BufferedImage image = null;
try
{
image = ImageIO.read(new File("lena512color.png"));
}
catch (IOException e)
{
e.printStackTrace();
return;
}
f.getContentPane().setLayout(new GridLayout(1,2));
f.getContentPane().add(new JLabel(new ImageIcon(image)));
f.getContentPane().add(new Pseudo3DImagePanel(image));
f.pack();
f.setLocationRelativeTo(null);
f.setVisible(true);
}
}
class Pseudo3DImagePanel extends JPanel
implements MouseListener, MouseMotionListener
{
private final BufferedImage inputImage;
private final Point2D p0;
private final Point2D p1;
private final Point2D p2;
private final Point2D p3;
private Point2D draggedPoint;
Pseudo3DImagePanel(BufferedImage inputImage)
{
this.inputImage = inputImage;
this.p0 = new Point2D.Double(30,20);
this.p1 = new Point2D.Double(50,400);
this.p2 = new Point2D.Double(450,300);
this.p3 = new Point2D.Double(430,100);
addMouseListener(this);
addMouseMotionListener(this);
}
@Override
protected void paintComponent(Graphics g)
{
super.paintComponent(g);
BufferedImage image = Pseudo3D.computeImage(inputImage, p0, p1, p2, p3);
g.drawImage(image, 0, 0, null);
int r = 8;
g.setColor(Color.RED);
g.fillOval((int)p0.getX()-r, (int)p0.getY()-r, r+r, r+r);
g.fillOval((int)p1.getX()-r, (int)p1.getY()-r, r+r, r+r);
g.fillOval((int)p2.getX()-r, (int)p2.getY()-r, r+r, r+r);
g.fillOval((int)p3.getX()-r, (int)p3.getY()-r, r+r, r+r);
}
@Override
public void mousePressed(MouseEvent e)
{
Point p = e.getPoint();
int r = 8;
if (p.distance(p0) < r) draggedPoint = p0;
if (p.distance(p1) < r) draggedPoint = p1;
if (p.distance(p2) < r) draggedPoint = p2;
if (p.distance(p3) < r) draggedPoint = p3;
}
@Override
public void mouseDragged(MouseEvent e)
{
if (draggedPoint != null)
{
draggedPoint.setLocation(e.getX(), e.getY());
repaint();
}
}
@Override
public void mouseReleased(MouseEvent e)
{
draggedPoint = null;
}
@Override
public void mouseMoved(MouseEvent e) {}
@Override
public void mouseClicked(MouseEvent e) {}
@Override
public void mouseEntered(MouseEvent e) {}
@Override
public void mouseExited(MouseEvent e) {}
}
class Pseudo3D
{
static BufferedImage computeImage(
BufferedImage image,
Point2D p0, Point2D p1, Point2D p2, Point2D p3)
{
int w = image.getWidth();
int h = image.getHeight();
BufferedImage result =
new BufferedImage(w, h, BufferedImage.TYPE_INT_ARGB);
Point2D ip0 = new Point2D.Double(0,0);
Point2D ip1 = new Point2D.Double(0,h);
Point2D ip2 = new Point2D.Double(w,h);
Point2D ip3 = new Point2D.Double(w,0);
Matrix3D m = computeProjectionMatrix(
new Point2D[] { p0, p1, p2, p3 },
new Point2D[] { ip0, ip1, ip2, ip3 });
Matrix3D mInv = new Matrix3D(m);
mInv.invert();
for (int y = 0; y < h; y++)
{
for (int x = 0; x < w; x++)
{
Point2D p = new Point2D.Double(x,y);
mInv.transform(p);
int ix = (int)p.getX();
int iy = (int)p.getY();
if (ix >= 0 && ix < w && iy >= 0 && iy < h)
{
int rgb = image.getRGB(ix, iy);
result.setRGB(x, y, rgb);
}
}
}
return result;
}
// From https://math.stackexchange.com/questions/296794
private static Matrix3D computeProjectionMatrix(Point2D p0[], Point2D p1[])
{
Matrix3D m0 = computeProjectionMatrix(p0);
Matrix3D m1 = computeProjectionMatrix(p1);
m1.invert();
m0.mul(m1);
return m0;
}
// From https://math.stackexchange.com/questions/296794
private static Matrix3D computeProjectionMatrix(Point2D p[])
{
Matrix3D m = new Matrix3D(
p[0].getX(), p[1].getX(), p[2].getX(),
p[0].getY(), p[1].getY(), p[2].getY(),
1, 1, 1);
Point3D p3 = new Point3D(p[3].getX(), p[3].getY(), 1);
Matrix3D mInv = new Matrix3D(m);
mInv.invert();
mInv.transform(p3);
m.m00 *= p3.x;
m.m01 *= p3.y;
m.m02 *= p3.z;
m.m10 *= p3.x;
m.m11 *= p3.y;
m.m12 *= p3.z;
m.m20 *= p3.x;
m.m21 *= p3.y;
m.m22 *= p3.z;
return m;
}
private static class Point3D
{
double x;
double y;
double z;
Point3D(double x, double y, double z)
{
this.x = x;
this.y = y;
this.z = z;
}
}
private static class Matrix3D
{
double m00;
double m01;
double m02;
double m10;
double m11;
double m12;
double m20;
double m21;
double m22;
Matrix3D(
double m00, double m01, double m02,
double m10, double m11, double m12,
double m20, double m21, double m22)
{
this.m00 = m00;
this.m01 = m01;
this.m02 = m02;
this.m10 = m10;
this.m11 = m11;
this.m12 = m12;
this.m20 = m20;
this.m21 = m21;
this.m22 = m22;
}
Matrix3D(Matrix3D m)
{
this.m00 = m.m00;
this.m01 = m.m01;
this.m02 = m.m02;
this.m10 = m.m10;
this.m11 = m.m11;
this.m12 = m.m12;
this.m20 = m.m20;
this.m21 = m.m21;
this.m22 = m.m22;
}
// From http://www.dr-lex.be/random/matrix_inv.html
void invert()
{
double invDet = 1.0/determinant();
double nm00 = m22 * m11 - m21 * m12;
double nm01 = -(m22 * m01 - m21 * m02);
double nm02 = m12 * m01 - m11 * m02;
double nm10 = -(m22 * m10 - m20 * m12);
double nm11 = m22 * m00 - m20 * m02;
double nm12 = -(m12 * m00 - m10 * m02);
double nm20 = m21 * m10 - m20 * m11;
double nm21 = -(m21 * m00 - m20 * m01);
double nm22 = m11 * m00 - m10 * m01;
m00 = nm00 * invDet;
m01 = nm01 * invDet;
m02 = nm02 * invDet;
m10 = nm10 * invDet;
m11 = nm11 * invDet;
m12 = nm12 * invDet;
m20 = nm20 * invDet;
m21 = nm21 * invDet;
m22 = nm22 * invDet;
}
// From http://www.dr-lex.be/random/matrix_inv.html
double determinant()
{
return
m00 * (m11 * m22 - m12 * m21) +
m01 * (m12 * m20 - m10 * m22) +
m02 * (m10 * m21 - m11 * m20);
}
final void mul(double factor)
{
m00 *= factor;
m01 *= factor;
m02 *= factor;
m10 *= factor;
m11 *= factor;
m12 *= factor;
m20 *= factor;
m21 *= factor;
m22 *= factor;
}
void transform(Point3D p)
{
double x = m00 * p.x + m01 * p.y + m02 * p.z;
double y = m10 * p.x + m11 * p.y + m12 * p.z;
double z = m20 * p.x + m21 * p.y + m22 * p.z;
p.x = x;
p.y = y;
p.z = z;
}
void transform(Point2D pp)
{
Point3D p = new Point3D(pp.getX(), pp.getY(), 1.0);
transform(p);
pp.setLocation(p.x/p.z, p.y/p.z);
}
void mul(Matrix3D m)
{
double nm00 = m00 * m.m00 + m01 * m.m10 + m02 * m.m20;
double nm01 = m00 * m.m01 + m01 * m.m11 + m02 * m.m21;
double nm02 = m00 * m.m02 + m01 * m.m12 + m02 * m.m22;
double nm10 = m10 * m.m00 + m11 * m.m10 + m12 * m.m20;
double nm11 = m10 * m.m01 + m11 * m.m11 + m12 * m.m21;
double nm12 = m10 * m.m02 + m11 * m.m12 + m12 * m.m22;
double nm20 = m20 * m.m00 + m21 * m.m10 + m22 * m.m20;
double nm21 = m20 * m.m01 + m21 * m.m11 + m22 * m.m21;
double nm22 = m20 * m.m02 + m21 * m.m12 + m22 * m.m22;
m00 = nm00;
m01 = nm01;
m02 = nm02;
m10 = nm10;
m11 = nm11;
m12 = nm12;
m20 = nm20;
m21 = nm21;
m22 = nm22;
}
}
}
+0
令人印象深刻的答案 - 剩下的就是某种反锯齿:-) – tucuxi
+0
非常有用的答案,确切的。 –
2
我不知道任何标准的Java实现,但下面的代码(使用LibGDX提供点和矩阵操作)适用于我。要获得转换矩阵,我使用getProjectionMatrix
;一旦我有了它,我可以使用类似于上面的transformPoints
的东西来转换点。您可以在第一张图像中为每个“方形像素”调用transformPoints
,并在第二张图像中获取相应“投影像素”的角点。这是缓慢的,但嘿,没有人强迫你不使用OpenGL ...
/**
* Transforms all points in a polygon using a 3x3 projection matrix.
*
* @param t
* the 3x3 transform matrix
* @param points
* the points to transform. Coordinates will be overwritten
*/
public static void transformPoints(Matrix3 t, Vector2... points) {
Vector3 v3 = new Vector3();
for (Vector2 v : points) {
v3.set(v.x, v.y, 1);
v3.mul(t);
v.set(v3.x/v3.z, v3.y/v3.z);
}
}
private static Matrix3 mapBasisToImage(Vector2[] v) {
// solve (v1 v2 v3) * <a b c> = v4 using <a b c> = (v1 v2 v3)^-1 * v4
Matrix3 v123 = new Matrix3(new float[] { v[0].x, v[0].y, 1, v[1].x,
v[1].y, 1, v[2].x, v[2].y, 1 });
Vector3 v4 = new Vector3(new float[] { v[3].x, v[3].y, 1 });
float[] M = v123.val.clone();
v4.mul(v123.inv());
// scale by solutions
for (int i = 0; i < 3; i++) {
M[i + 0] *= v4.x;
M[i + 3] *= v4.y;
M[i + 6] *= v4.z;
}
Matrix3 bti = new Matrix3(M);
return bti;
}
/**
* Calculates a projection matrix from two corresponding sets of four
* non-collinear 2d vertices. Notice that "view" and "world" are actually
* interchangeable. Use sparingly: several intermediate matrices are
* required, and performance may suffer if called in a tight loop.
*
* @param view
* four points in the "view" (a camera pointed at the world,
* probably with some kind of perspective distortion)
* @param world
* four corresponding points in the "world" (where distances and
* angles are correct)
* @return a 3d projection that can be used to transform any view-based 2d
* vector into 'real space', and inverted to undo the process.
* @see <a href="http://jsfiddle.net/dFrHS/1/">this example</a>, referenced
* and described an excellent @see <a
* href="http://math.stackexchange.com/questions/296794/">
* math.stackexchange.com answer</a>.
*/
public static Matrix3 getProjectionMatrix(Vector2[] view, Vector2[] world) {
Matrix3 A = mapBasisToImage(view);
Matrix3 B = mapBasisToImage(world);
// combined - translates any vector from v-space to w-space
return B.mul(A.inv());
}
将其转换为标准的Java类应该很容易(虽然标准Java没有三维点,你只需要X,Y和z;并且有很多简单的矩阵求逆运算库)。
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你有什么试过的?你想写的方法的输入和输出是什么?你想如何指定转换?你至少需要一个3x3的矩阵(因为一个2x2矩阵只适用于仿射变换,而你的看起来像我的透视图)... – tucuxi
我需要变形BufferedImage或像素数组(int [] rgbs) –
有什么方法可以指定应该如何转化?你*必须考虑这些细节。 – tucuxi