java - 中点位移地形伪影

Question

我正在尝试用 Java 实现中点位移算法。它也被称为菱形方 block 算法。我的引用是 http://www.lighthouse3d.com/opengl/terrain/index.php3?mpd .除了右边缘和下边缘外，它似乎可以正常工作。

See Midpoint Displacement Results

仔细观察，可以看到“粗糙”的边缘。谁能指出哪里出了问题？在该算法的其他在线实现中尚未观察到这种效果。

代码

private void generateWorldMPD() {               
    /* The following is my first attempt at the MDP algorithm. */       

    // displacement boundary.
    double displacementBound = Constants.DEFAULT_ROUGHNESS_CONSTANT;
    double[][] A = Utilities.get2DDoubleArray(Constants.MPD_PRESET_HEIGHT, 2, 2);
    int iterations =0;
    while (iterations < mPDIterations) {

        // create a new array large enough for the new points being added.
        double [][] B = new double[A.length * 2 - 1][A[0].length * 2 - 1];

        // move the points in A to B, skipping every other element as space for a new point
        for (int i = 0; i < B.length; i +=2) 
            for (int j = 0; j < B[i].length; j+=2) {
                B[i][j] = A[i / 2][j / 2];                  
            }

        //calculate the height of each new center point as the average of the four adjacent elements  
        //(diamond step) and add a random displacement to each
        for (int i = 1; i < B.length; i+= 2)
            for (int j = 1; j < B[i].length; j+=2)  {
                averageFromCornersAndDisplace(B, i, j, displacementBound);

            }

        //calculate the height of each new non-center point (square step) and add a random displacement to each
        for (int i = 0; i < B.length; i ++)
            for (int j = 0; j < B[i].length; j++)
                if (i % 2 == 0)         //on every even row, calculate for only odd columns
                    if (j % 2 == 0) continue;
                    else
                        averageFromAdjAndDisplace( B , i, j, displacementBound );

            else                                //on every odd row, calculate for only even columns
                    if (j % 2 == 0)
                        averageFromAdjAndDisplace( B , i, j, displacementBound );
                    else
                        continue;

        displacementBound *= Math.pow(2, -Constants.DEFAULT_ROUGHNESS_CONSTANT);

        // assign B to A            
        A = B;

        iterations++;
    }
}

private void averageFromCornersAndDisplace(double[][] A, int i, int j, double displacementBoundary) {
    double nw = A[ wrap(i - 1, 0, A.length - 1) ][ wrap(j - 1, 0, A[i].length - 1) ];
    double ne = A[ wrap(i + 1, 0, A.length - 1) ][ wrap(j - 1, 0, A[i].length - 1) ];
    double sw = A[ wrap(i - 1, 0, A.length - 1) ][ wrap(j + 1, 0, A[i].length - 1) ];
    double se = A[ wrap(i + 1, 0, A.length - 1) ][ wrap(j + 1, 0, A[i].length - 1) ];
    A[i][j] = (nw + ne + sw + se) / 4;  
    A[i][j] += randomDisplacement(displacementBoundary);
}

private void averageFromAdjAndDisplace(double[][] A, int i, int j, double displacementBoundary) {
    double north = A[i][ wrap(j - 1, 0, A[i].length - 1)];
    double south = A[i][ wrap(j + 1, 0, A[i].length - 1)];
    double west  = A[ wrap(i - 1, 0, A.length - 1) ][j];
    double east  = A[ wrap(i + 1, 0, A.length - 1) ][j];
    A[i][j] = (north + south + east + west) / 4;    
    A[i][j] += randomDisplacement(displacementBoundary);
}

// This function returns a value that is wrapped around the interval if
// it exceeds the given bounds in the negative or positive direction.
private int wrap(int n, int lowerBound, int upperBound) {

    int lengthOfInterval = upperBound - lowerBound;

    if (n < lowerBound) 
        return (lowerBound - n) % lengthOfInterval;
    else
        return (n - upperBound) % lengthOfInterval; 
}

注释

private void generateWorldMPD() {               
    /* The following is my first attempt at the MDP algorithm. */       

    // displacement boundary.
    double displacementBound = Constants.DEFAULT_ROUGHNESS_CONSTANT;
    double[][] A = Utilities.get2DDoubleArray(Constants.MPD_PRESET_HEIGHT, 2, 2);
    int iterations =0;

这部分定义了一个变量 displacementBound，一个初始化为默认值的 double 二维数组，以及另一个名为 iterations 的变量。

while (iterations < mPDIterations) {

    // create a new array large enough for the new points being added.
    double [][] B = new double[A.length * 2 - 1][A[0].length * 2 - 1];

    // move the points in A to B, skipping every other element as space for a new point
    for (int i = 0; i < B.length; i +=2) 
        for (int j = 0; j < B[i].length; j+=2) {
            B[i][j] = A[i / 2][j / 2];                  
        }

这部分是声明循环的地方。它将运行 mPDIterations 循环。创建了一个临时数组 B 来保存 A 的更新版本，使 B 大于 A 以保存新版本数据点。之后有两个 for 循环，一个嵌套在另一个循环中，将 A 的当前值放入临时 B，注意每隔一行和每一列保留空白的。看看这个例子:

// The '*'s represent a cell in an array that is populated with a value.
// The '_'s represent a cell in an array that is empty.

// This is 'A'.
* *
* *

// This is 'B'. At the moment, completely empty.
_ _ _ 
_ _ _ 
_ _ _ 

// The elements of 'A' are tranferred to 'B'.
// Blank cells are inserted in every other row, and every other column.
* _ * 
_ _ _ 
* _ * 

现在是下一段代码:

        //calculate the height of each new center point as the average of the four adjacent elements  
        //(diamond step) and add a random displacement to each
        for (int i = 1; i < B.length; i+= 2)
            for (int j = 1; j < B[i].length; j+=2)  {
                averageFromCornersAndDisplace(B, i, j, displacementBound);

            }

在此部分中，中心 处的每个点指的是在北、南<的每个主要方向上都有一个空的相邻单元格的单元格/strong>、东 和西 的值是四个相邻角 点的平均值和随机位移值 添加到它。这称为菱形步骤。阐明什么是“中心”:

// The big "O" indicates the 'center' in this 2D array.
* _ *
_ O _
* _ *

下一个代码部分:

//calculate the height of each new non-center point (square step) and add a random displacement to each
for (int i = 0; i < B.length; i ++)
    for (int j = 0; j < B[i].length; j++)
        if (i % 2 == 0)         //on every even row, calculate for only odd columns
            if (j % 2 == 0) continue;
            else
                averageFromAdjAndDisplace( B , i, j, displacementBound );

    else                                //on every odd row, calculate for only even columns
            if (j % 2 == 0)
                averageFromAdjAndDisplace( B , i, j, displacementBound );
            else
                continue;

这部分与上一段代码类似。它为每个非中心点和空点分配一个新值；该值是主要方向北、南、东和西中相邻元素的平均值，添加了另一个随机位移值。这称为方步。上面的代码确保只有非中心点和空点被赋予新值；这些要点等同于侧要点，如下所述:

// The big 'O's indicate the 'side points' in this 2D array.
* O *
O * O
* O *

结束 while 循环的部分如下:

        displacementBound *= Math.pow(2, -Constants.DEFAULT_ROUGHNESS_CONSTANT);

        // assign B to A            
        A = B;

        iterations++;
    } // end of while loop

根据上述文章中给出的信息，变量 displacementBound 在上面的部分中被减少，其中包括 while 循环的结束。 A 的内容通过在开始另一次循环迭代或终止循环之前将 B 的更新内容分配给 A 来更新。A p>

最后，辅助方法 averageFromCornersAndDisplace()、averageFromSidesAndDisplace() 和 wrap() 已包含在内，但对它们的额外解释是不必要。 randomDisplacement() 方法根本没有包含在内。供您引用，它返回一个随机 float x，以给定数 b 为界:

// The method returns a double x, where -b <= x < b
double randomDisplacement(double b);

Answer 1

我刚刚看到你的帖子弹出，我想你已经整理好了。不管怎样，如果你想做这样的包装，有一个巧妙的技巧可以解决负面模组在 C/Java 中不能正常工作的事实。您所做的只是将模数的一些倍数(注意不要溢出)加回数字以确保它是非负数。然后你可以像往常一样修改而不会破坏。这是一个例子:

private int wrap(int n, int lowerBound, int upperBound) {
    int lengthOfInterval = upperBound - lowerBound;
    return lowerBound + ((n - lowerBound + lengthOfInterval) % lengthOfInterval);
}