我已经实现了一个生成高度图的 Diamond-Square 函数。乍一看,该实现似乎工作正常。
这只是两个示例,但已经可以看出输出值总体上似乎相当高。只有很少的真正黑暗的值(value)观。一世。 E. 如果您查看此 paper 中的高度图(由 diamond square 制作)你可以看到它们不像我的那么均匀。不同地区之间有更多的偏移量。有些区域看起来像陨石坑。
我无法弄清楚此行为的原因是错误的参数化还是实现。尽管 Web 上的示例实现确实略有不同,但我认为我已经掌握了基本思路。
我正在处理平面类型数组。我传递给函数的参数是:
边长
最大高度
粗糙度
我正在调用 Heightmap 函数以获得输出:
/**
* Creates a heightmap based on parameters passed.
* @param {number} sideLength - Side length of a the resulting grid array. Diamond-Square can only have a size (2^n)+1.
* @param {number} maxHeight - Max height value for the heightmap's values.
* @param {number} roughness - A factor which is used as offset value for the heightmap. Defines the roughness of a heightmap.
* @returns {Float32Array} - A flat `Float32Array` representing a 2D-grid with size `sideLength * sideLength`.
*/
static HeightMap(sideLength, maxHeight, roughness) {
const n = Math.log(sideLength - 1) / Math.log(2);
if (n < 0 || n % 1 != 0) {
throw "Invalid side length in Diamond Square: Side Length has to be in range of `(2^n) + 1`.";
}
let gridArray = new Float32Array(sideLength * sideLength);
this._initGrid(gridArray, sideLength, maxHeight);
this._seed(gridArray, sideLength, roughness);
return gridArray;
}
这里首先启动“网格”:
/**
* Sets the initial corner values for a Diamond-Square grid.
* @param {Float32Array} gridArray - An `Float32Array` with its values (ideally) set to `0`.
* @param {number} sideLength - Side length of a the resulting grid array. Diamond-Square can only have a size `(2^n)+1`.
* @param {number} maxHeight - Max height value for the heightmap's values.
* @returns {Float32Array} - A flat `Float32Array` representing a 2D-grid with its NW, NE, SE and SW values initialized.
*/
static _initGrid(gridArray, sideLength, maxHeight) {
gridArray[0] = MathHelper.RandomInt(0, maxHeight); // NW
gridArray[sideLength - 1] = MathHelper.RandomInt(0, maxHeight); // NE
gridArray[sideLength * sideLength - 1] = MathHelper.RandomInt(0, maxHeight); // SE
gridArray[sideLength * sideLength - sideLength] = MathHelper.RandomInt(0, maxHeight); // SW
return gridArray;
}
之后 HeightMap 函数调用 _seed,这基本上是 Diamond-Square 循环:
/**
* Performs the Diamond Square (aka. Midpoint displacement) algorithm on a given flat TypedArray.
* @param {Float32Array} gridArray - An (Diamond-Square-initialized) `Float32Array`.
* @param {number} sideLength - Side length of a the resulting grid array.
* @param {number} roughness - A factor which is used as offset value for the heightmap. Defines the roughness of a heightmap.
* @returns {Float32Array} - Returns a ready to use heightmap produced by the Diamond-Square algorithm.
*/
static _seed(gridArray, sideLength, roughness) {
let step = Math.sqrt(gridArray.length) - 1;
let size = Math.sqrt(gridArray.length) - 1;
let currentRoughness = roughness;
while (step / 2 >= 1) {
let numSquares = (Math.pow(size, 2)) / (Math.pow(step, 2));
let perRowSquares = Math.floor(Math.sqrt(numSquares));
for (let i = 0; i < perRowSquares; i++) {
for (let j = 0; j < perRowSquares; j++) {
const nwIndex = this._getNWIndex(i, j, step, sideLength);
const cornerValues = this._getCornerValues(nwIndex, gridArray, sideLength, step);
this._diamondStep(nwIndex, cornerValues, gridArray, sideLength, step, currentRoughness);
this._squareStep(nwIndex, cornerValues, gridArray, sideLength, step, currentRoughness);
}
}
currentRoughness /= 2.0;
step /= 2;
}
return gridArray;
}
请注意,我正在根据当前西北指数的指数计算位置指数。为此,我有一个功能:
/**
* Returns the array index for the north-west value for the current step.
* @param {number} i - Current row, I guess.
* @param {number} j - Current column, I guess.
* @param {number} stepSize - Current step size.
* @param {number} sideLength - Grid's side length.
* @returns {number} - Returns the index for current north-west value.
*/
static _getNWIndex(i, j, stepSize, sideLength) {
return (i * (stepSize * sideLength)) + j * stepSize;
}
因为所有四个 Angular 值都用在菱形和方形步骤中,所以我也有一个函数:
/**
* Return an array holding the north-west, north-east, south-west and south-east values for the current step.
* @param {number} nwIndex - North-West index for current step.
* @param {Float32Array} gridArray - The corner values for the current step.
* @param {number} sideLength - Grid's side length.
* @param {number} stepSize - Current step size.
* @returns {Float32Array} - Returns the typed array the function of operating on.
*/
static _getCornerValues(nwIndex, gridArray, sideLength, stepSize) {
return [
gridArray[nwIndex], // NW
gridArray[nwIndex + stepSize], // NE
gridArray[nwIndex + stepSize * sideLength], // SW
gridArray[nwIndex + stepSize + stepSize * sideLength] // SE
];
}
最后但同样重要的是,我有 _diamondStep 和 _sqaureStep:
/**
* Performs the Diamond Step by setting the center value for the current step.
* @param {number} nwIndex - North-West index for current step.
* @param {number[]} cornerValues - The corner values for the current step.
* @param {Float32Array} gridArray - Array holding heightmap data. Function will write to this array.
* @param {number} sideLength - Grid's side length.
* @param {number} stepSize - Current step size.
* @returns {Float32Array} - Returns the typed array the function of operating on.
*/
static _diamondStep(nwIndex, cornerValues, gridArray, sideLength, stepSize, roughness) {
// Center point. Calculated from "East - `stepSize / 2`"
gridArray[(((nwIndex + stepSize * sideLength) + stepSize) - (stepSize * sideLength) / 2) - stepSize / 2]
= (cornerValues[0] + cornerValues[1] + cornerValues[2] + cornerValues[3]) / 4 + (roughness * MathHelper.RandomInt(-1, 1));
return gridArray;
}
/**
* Performs the Square Step by setting the north, east, south and west values for the current step.
* @param {number} nwIndex - North-West index for current step.
* @param {number[]} cornerValues - The corner values for the current step.
* @param {Float32Array} gridArray - Array holding heightmap data. Function will write to this array.
* @param {number} sideLength - Grid's side length.
* @param {number} stepSize - Current step size.
* @param {number} roughness - Roughness factor for the current step.
* @returns {Float32Array} - Returns the typed array the function of operating on.
*/
static _squareStep(nwIndex, cornerValues, gridArray, sideLength, stepSize, roughness) {
const average = (cornerValues[0] + cornerValues[1] + cornerValues[2] + cornerValues[3]) / 4;
const value = average + (roughness * MathHelper.RandomInt(-1, 1));
// N
gridArray[nwIndex + (stepSize / 2)] = value;
// E
gridArray[((nwIndex + stepSize * sideLength) + stepSize) - (stepSize * sideLength) / 2] = value;
// S
gridArray[(nwIndex + stepSize * sideLength) + stepSize / 2] = value;
// W
gridArray[(nwIndex + stepSize * sideLength) - (stepSize * sideLength) / 2] = value;
return gridArray;
}
正如我之前提到的,该实现似乎有效。我仍然想知道整体“白度”是否是由错误的参数化或错误的实现引起的?
这是一个有效的 fiddle :
function HeightMap(sideLength, maxHeight, roughness) {
const n = Math.log(sideLength - 1) / Math.log(2);
if (n < 0 || n % 1 != 0) {
throw "Invalid side length in Diamond Square: Side Length has to be in range of `(2^n) + 1`.";
}
let gridArray = new Float32Array(sideLength * sideLength);
_initGrid(gridArray, sideLength, maxHeight);
_seed(gridArray, sideLength, roughness);
return gridArray;
}
function _initGrid(gridArray, sideLength, maxHeight) {
gridArray[0] = RandomInt(0, maxHeight); // NW
gridArray[sideLength - 1] = RandomInt(0, maxHeight); // NE
gridArray[sideLength * sideLength - 1] = RandomInt(0, maxHeight); // SE
gridArray[sideLength * sideLength - sideLength] = RandomInt(0, maxHeight); // SW
return gridArray;
}
function _seed(gridArray, sideLength, roughness) {
let step = Math.sqrt(gridArray.length) - 1;
let size = Math.sqrt(gridArray.length) - 1;
let currentRoughness = roughness;
while (step / 2 >= 1) {
let numSquares = (Math.pow(size, 2)) / (Math.pow(step, 2));
let perRowSquares = Math.floor(Math.sqrt(numSquares));
for (let i = 0; i < perRowSquares; i++) {
for (let j = 0; j < perRowSquares; j++) {
const nwIndex = _getNWIndex(i, j, step, sideLength);
const cornerValues = _getCornerValues(nwIndex, gridArray, sideLength, step);
_diamondStep(nwIndex, cornerValues, gridArray, sideLength, step, currentRoughness);
_squareStep(nwIndex, cornerValues, gridArray, sideLength, step, currentRoughness);
}
}
currentRoughness /= 2.0;
step /= 2;
}
return gridArray;
}
function _diamondStep(nwIndex, cornerValues, gridArray, sideLength, stepSize, roughness) {
gridArray[(((nwIndex + stepSize * sideLength) + stepSize) - (stepSize * sideLength) / 2) - stepSize / 2] =
(cornerValues[0] + cornerValues[1] + cornerValues[2] + cornerValues[3]) / 4 + (roughness * RandomInt(-1, 1));
return gridArray;
}
function _squareStep(nwIndex, cornerValues, gridArray, sideLength, stepSize, roughness) {
const average = (cornerValues[0] + cornerValues[1] + cornerValues[2] + cornerValues[3]) / 4;
const value = average + (roughness * RandomInt(-1, 1));
// N
gridArray[nwIndex + (stepSize / 2)] = value;
// E
gridArray[((nwIndex + stepSize * sideLength) + stepSize) - (stepSize * sideLength) / 2] = value;
// S
gridArray[(nwIndex + stepSize * sideLength) + stepSize / 2] = value;
// W
gridArray[(nwIndex + stepSize * sideLength) - (stepSize * sideLength) / 2] = value;
return gridArray;
}
function _getCornerValues(nwIndex, gridArray, sideLength, stepSize) {
return [
gridArray[nwIndex], // NW
gridArray[nwIndex + stepSize], // NE
gridArray[nwIndex + stepSize * sideLength], // SW
gridArray[nwIndex + stepSize + stepSize * sideLength] // SE
];
}
function _getNWIndex(i, j, stepSize, sideLength) {
return (i * (stepSize * sideLength)) + j * stepSize;
}
function GenerateIterations(max) {
let iterations = [];
for (let n = 0; n < max; n++) {
iterations.push(Math.pow(2, n) + 1);
}
return iterations;
}
function Grayscale(canvasName, data, rows, cols) {
let canvas = document.getElementById(canvasName);
let ctx = canvas.getContext("2d");
let imageData = ctx.createImageData(cols, rows);
for (let i = 0; i < data.length; i++) {
const color = data[i];
imageData.data[i * 4] = color;
imageData.data[i * 4 + 1] = color;
imageData.data[i * 4 + 2] = color;
imageData.data[i * 4 + 3] = 255;
}
ctx.putImageData(imageData, 0, 0);
}
function RandomInt(min, max) {
return Math.floor(Math.random() * (max - min + 1)) + min;
}
let terrainGrid = HeightMap(257, 255, 50);
Grayscale('grayscaleCanvas', terrainGrid, 257, 257);.greyscaleCanvas {
border: solid 1px black;
}<canvas id="grayscaleCanvas" class="greyscaleCanvas" width="257px" height="257px"></canvas>
最佳答案
因此,我根据我对该算法工作原理的理解对代码进行了一些修改。这完全有可能仍然无法正常工作,但我认为不管怎样,这段代码都会让您更容易使用。
根据我在维基百科上阅读的菱形方形步骤的理解,我想我也发现了您的算法中的一些问题:
function HeightMap(sideLength, maxHeight, roughness) {
const n = Math.log(sideLength - 1) / Math.log(2);
if (n < 0 || n % 1 != 0) {
throw "Invalid side length in Diamond Square: Side Length has to be in range of `(2^n) + 1`.";
}
let gridArray = new Array(sideLength);
for (var i = 0; i < gridArray.length; i++) {
gridArray[i] = new Float32Array(sideLength);
}
gridArray = _initGrid(gridArray, sideLength, maxHeight);
gridArray = _seed(gridArray, sideLength, roughness);
return gridArray;
}
function _initGrid(gridArray, sideLength, maxHeight) {
gridArray[0][0] = RandomInt(0, maxHeight); // NW
gridArray[0][sideLength-1] = RandomInt(0, maxHeight); // NE
gridArray[sideLength-1][sideLength-1] = RandomInt(0, maxHeight); // SE
gridArray[sideLength-1][0] = RandomInt(0, maxHeight); // SW
return gridArray;
}
function _seed(gridArray, sideLength, roughness) {
let step = sideLength - 1;
let size = sideLength - 1;
let currentRoughness = roughness;
let run_num = 0
while (step / 2 >= 1) {
console.log(run_num)
run_num = run_num + 1
let numSquares = Math.pow(size, 2) / Math.pow(step, 2);
let perRowSquares = Math.floor(Math.sqrt(numSquares));
for (let i = 0; i < perRowSquares; i++) {
for (let j = 0; j < perRowSquares; j++) {
row = i*step
col = j*step
const squareCornerValues = _getSquareCornerValues(gridArray, row, col, step)
gridArray = _diamondStep(squareCornerValues, row, col, step, gridArray, currentRoughness);
gridArray = _squareStep(row, col, step, gridArray, sideLength, currentRoughness)
// _squareStep(diamondMidPoints, gridArray, step, currentRoughness);
}
}
currentRoughness /= 2.0;
step /= 2;
}
return gridArray;
}
function _diamondStep(squareCornerValues, i, j, step, gridArray, currentRoughness) {
gridArray[row+step/2][col+step/2] = (squareCornerValues[0] + squareCornerValues[1] + squareCornerValues[2] + squareCornerValues[3] ) / 4 + (currentRoughness * RandomInt(-1, 1));
return gridArray;
}
function _squareStep(row, col, step, gridArray, sideLength, currentRoughness) {
let diamondMidPoints = [[row, col+step/2], //top
[row+step/2, col], //left
[row+step, col+step/2], //right
[row+step/2, col+step] //bottom
];
for (let z = 0; z < diamondMidPoints.length; z++){
corners = _get_diamond_corners(diamondMidPoints[z], step, sideLength, gridArray);
gridArray[diamondMidPoints[z][0]][diamondMidPoints[z][1]] = (corners[0] + corners[1] + corners[2] + corners[3]) /4 + (currentRoughness * RandomInt(-1, 1));
}
return gridArray;
}
function _getSquareCornerValues(gridArray, row, col, step) {
return [
gridArray[row][col], // NW
gridArray[row][col+step], // NE
gridArray[row+step][col], // SW
gridArray[row+step][col+step] // SE
];
}
function _get_diamond_corners(diamondMidPoints, step, sideLength, gridArray){
row = diamondMidPoints[0];
col = diamondMidPoints[1];
top_coord = [(row - step/2 + sideLength) % sideLength, col];
left_coord = [row, (col - step/2 + sideLength) % sideLength];
right_coord = [row, (col + step/2 + sideLength) % sideLength];
bottom_coord = [(row + step/2 + sideLength) % sideLength, col];
return [gridArray[top_coord[0]][top_coord[1]],
gridArray[left_coord[0]][left_coord[1]],
gridArray[right_coord[0]][right_coord[1]],
gridArray[bottom_coord[0]][bottom_coord[1]]
];
}
function Grayscale(canvasName, data, rows, cols) {
let canvas = document.getElementById(canvasName);
let ctx = canvas.getContext("2d");
let imageData = ctx.createImageData(cols, rows);
for (let i = 0; i < data.length; i++) {
const color = data[i];
imageData.data[i * 4] = color;
imageData.data[i * 4 + 1] = color;
imageData.data[i * 4 + 2] = color;
imageData.data[i * 4 + 3] = 255;
}
ctx.putImageData(imageData, 0, 0);
}
function RandomInt(min, max) {
return Math.floor(Math.random() * (max - min + 1)) + min;
}
let terrainGrid = HeightMap(257, 255, 50);
terrainList = []
for (let q=0; q < 257; q++) {
terrainList.push.apply(terrainList, terrainGrid[q])
}
Grayscale('grayscaleCanvas', terrainList, 257, 257);
我做的第一件事是将其更改为使用二维数组索引。这使得平方步的平均更容易(我能够更简单地环绕矩阵的边缘)。
我还更改了它以使用数组中的实际行值和列值,这比 block 坐标更简单。
我认为您最初没有正确计算平方步。您使用的 Angular 与菱形步相关,但您只是对方形步的 Angular 进行平均,而不是根据计算出的中点值和 Angular 的相关子集找到平均值(请参阅菱形方形上的维基百科图像以查看什么我是说)。
这是一个包含所有内容的 JSFiddle,希望这是您想要的。 (注意:如果有任何事情没有按惯用方式完成,那是因为我不擅长 Javascript):https://jsfiddle.net/z6so4xyc/15/
关于javascript - Diamond-Square 实现产生的值(value)太高,我们在Stack Overflow上找到一个类似的问题: https://stackoverflow.com/questions/53195820/
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