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<h1 id="height-maps">高度图（Height Maps）</h1>
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<p>本章中我们将学习如何使用高度图创建复杂的地形。在开始前，你会注意到我们做了一些重构。我们创建了一些新的包和移动了一些类以更好地组织它们。你可以在源代码中了解这些改变。</p>
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<p>所以什么是高度图？高度图是用于生成三维地形的图像，它使用像素颜色来获取表面高度。高度图图像通常是灰度图，它可以由<a href="http://planetside.co.uk/">Terragen</a>等软件生成。一张高度图图像看起来就像这样。</p>
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<p><img alt="高度图" src="../_static/14/heightmap.png" /> </p>
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<p>上图就像你俯视一片陆地一样。利用上图，我们将构建由顶点组成的三角形所组成的网格。每个顶点的高度将根据图像的每个像素的颜色来计算。黑色是最低，白色是最高。</p>
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<p>我们将为图像的每个像素创建一组顶点，这些顶点将组成三角形，这些三角形将组成下图所示的网格。</p>
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<p><img alt="高度图网格" src="../_static/14/heightmap_grid.png" /> </p>
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<p>网格将组成一个巨大的四边形，它将会在X和Z轴上渲染，并根据像素颜色来改变它的Y轴高度。</p>
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<p><img alt="高度图坐标系" src="../_static/14/heightmap_coordinates.png" /> </p>
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<p>由高度图创建三维地形的过程可概括为以下步骤：
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* 加载储存高度图的图像(我们将使用一个<code>BufferedImage</code>实例以获取每个像素)。
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* 为每个图像像素创建一个顶点，其高度基于像素颜色。
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* 将正确的纹理坐标分配给顶点。
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* 设置索引以绘制与顶点相关的三角形。</p>
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<p>我们将创建一个名为<code>HeightMapMesh</code>的类，该类将基于高度图按以上步骤创建一个<code>Mesh</code>。让我们先看看该类定义的常量：</p>
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<pre><code class="language-java">private static final int MAX_COLOUR = 255 * 255 * 255;
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</code></pre>
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<p>如上所述，我们将基于高度图图像的每个像素的颜色来计算每个顶点的高度。图像通常是灰度图，对于PNG图像来说，这意味着每个像素的每个RGB值可以在0到255之间变化，因此我们有256个值来表示不同的高度。这可能足够了，但如果精度不够，我们可以使用三个RGB值以有更多的值，在此情况下，高度计算范围为0到255^3。我们将使用第二种方法，因此我们不局限于灰度图。</p>
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<p>接下来的常量是：</p>
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<pre><code class="language-java">private static final float STARTX = -0.5f;
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private static final float STARTZ = -0.5f;
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</code></pre>
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<p>网格将由一组顶点（一个顶点对应一个像素）构成，其X和Z坐标的范围如下
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* X轴的范围为[-0.5, 0.5]，即[<code>STARTX</code>, <code>-STARTX</code>]。
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* Z轴的范围为[-0.5, 0.5]，即[<code>STARTZ</code>, <code>-STARTZ</code>]。</p>
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<p>不用太过担心这些值，稍后得到的网格可以被缩放以适应世界的大小。关于Y轴，我们将设置<code>minY</code>和<code>maxY</code>两个参数，用于设置Y坐标的最低和最高值。这些参数并不是常数，因为我们可能希望在运行时更改它们，而不使用缩放。最后，地形将包含在范围为<code>[STARTX, -STARTX]</code>，<code>[minY, maxY]</code>，<code>[STARTZ, -STARTZ]</code>的立方体内。</p>
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<p>网格将会在<code>HeightMapMesh</code>类的构造函数中创建，该类的定义如下。</p>
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<pre><code class="language-java">public HeightMapMesh(float minY, float maxY, String heightMapFile, String textureFile, int textInc) throws Exception {
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</code></pre>
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<p>它接收Y轴的最小值和最大值，被用作高度图的图像文件名和要使用的纹理文件名。它还接受一个名为<code>textInc</code>的整数，这稍后再说明。</p>
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<p>我们在构造函数中做的第一件事就是将高度图图像加载到<code>BufferedImage</code>实例中。</p>
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<pre><code class="language-java">this.minY = minY;
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this.maxY = maxY;
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PNGDecoder decoder = new PNGDecoder(getClass().getResourceAsStream(heightMapFile));
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int height = decoder.getHeight();
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int width = decoder.getWidth();
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ByteBuffer buf = ByteBuffer.allocateDirect(
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4 * decoder.getWidth() * decoder.getHeight());
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decoder.decode(buf, decoder.getWidth() * 4, PNGDecoder.Format.RGBA);
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buf.flip();
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</code></pre>
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<p>然后，我们将纹理文件载入到一个<code>ByteBuffer</code>中，并设置构造<code>Mesh</code>所需的变量。<code>incx</code>和<code>incz</code>变量将储存每个顶点的X或Z坐标之间的最小间隔，因此<code>Mesh</code>包含在上述区域中。</p>
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<pre><code class="language-java">Texture texture = new Texture(textureFile);
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float incx = getWidth() / (width - 1);
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float incz = Math.abs(STARTZ * 2) / (height - 1);
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List<Float> positions = new ArrayList();
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List<Float> textCoords = new ArrayList();
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List<Integer> indices = new ArrayList();
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</code></pre>
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<p>之后，我们将遍历图像，为每个像素创建一个顶点，设置其纹理坐标与索引，以正确地定义组成<code>Mesh</code>的三角形。</p>
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<pre><code class="language-java">for (int row = 0; row < height; row++) {
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for (int col = 0; col < width; col++) {
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// 为当前位置创建顶点
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positions.add(STARTX + col * incx); // x
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positions.add(getHeight(col, row, width, buf)); // y
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positions.add(STARTZ + row * incz); // z
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// 设置纹理坐标
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textCoords.add((float) textInc * (float) col / (float) width);
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textCoords.add((float) textInc * (float) row / (float) height);
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// 创建索引
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if (col < width - 1 && row < height - 1) {
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int leftTop = row * width + col;
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int leftBottom = (row + 1) * width + col;
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int rightBottom = (row + 1) * width + col + 1;
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int rightTop = row * width + col + 1;
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indices.add(rightTop);
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indices.add(leftBottom);
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indices.add(leftTop);
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indices.add(rightBottom);
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indices.add(leftBottom);
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indices.add(rightTop);
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}
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}
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}
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</code></pre>
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<p>创建顶点坐标的过程是不需要解释的。现在先别管为什么我们用一个数字乘以纹理坐标以及如何计算高度。你可以看到，对于每个顶点，我们定义两个三角形的索引(除非现在是最后一行或最后一列)。让我们用一个<strong>3×3</strong>的图像来想象它们是如何构造的。一个<strong>3×3</strong>的图像包含9个顶点，每因此有<strong>2×4</strong>个三角形组成4个正方形。下图展示了网格，每个顶点被命名为<code>Vrc</code>(r：行，c：列)。</p>
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<p><img alt="高度图顶点" src="../_static/14/heightmap_vertices.png" /></p>
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<p>当处理第一个顶点(V00)时，我们在红色阴影处定义了两个三角形的索引。</p>
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<p><img alt="高度图索引I" src="../_static/14/heightmap_indices_i.png" /> </p>
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<p>当处理第二个顶点(V01)时，我们在红色阴影处又定义了两个三角形的索引。但当处理第三个顶点(V02)时，我们不需要定义更多的索引，该行的所有三角形都已被定义。</p>
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<p><img alt="高度图索引II" src="../_static/14/heightmap_indices_ii.png" /> </p>
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<p>你可以很容易地想到其他顶点的处理过程是如何进行的。现在，一旦创建了所有的顶点位置、纹理坐标和索引，我们就只需要用所有这些数据创建<code>Mesh</code>和相关的<code>Material</code>。</p>
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<pre><code class="language-java">float[] posArr = Utils.listToArray(positions);
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int[] indicesArr = indices.stream().mapToInt(i -> i).toArray();
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float[] textCoordsArr = Utils.listToArray(textCoords);
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float[] normalsArr = calcNormals(posArr, width, height);
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this.mesh = new Mesh(posArr, textCoordsArr, normalsArr, indicesArr);
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Material material = new Material(texture, 0.0f);
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mesh.setMaterial(material);
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</code></pre>
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<p>你可以看到，我们根据顶点位置计算法线。在看如何计算法线之前，来看看如何获取高度吧。我们已经创建了一个名为<code>getHeight</code>的方法，它负责计算顶点的高度。</p>
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<pre><code class="language-java">private float getHeight(int x, int z, int width, ByteBuffer buffer) {
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byte r = buffer.get(x * 4 + 0 + z * 4 * width);
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byte g = buffer.get(x * 4 + 1 + z * 4 * width);
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byte b = buffer.get(x * 4 + 2 + z * 4 * width);
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byte a = buffer.get(x * 4 + 3 + z * 4 * width);
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int argb = ((0xFF & a) << 24) | ((0xFF & r) << 16)
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| ((0xFF & g) << 8) | (0xFF & b);
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return this.minY + Math.abs(this.maxY - this.minY) * ((float) argb / (float) MAX_COLOUR);
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}
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</code></pre>
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<p>该方法接受像素的X和Y坐标，图像的宽度以及与之相关的<code>ByteBuffer</code>，返回RGB颜色(R、G、B分量之和)并计算包含在<code>minY</code>和<code>maxY</code>之间的值(<code>minY</code>为黑色，<code>maxY</code>为白色)。</p>
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<p>你可以使用<code>BufferedImage</code>来编写一个更简单的方法，它有更方便的方法来获得RGB值，但这将使用AWT。记住AWT不能很好的兼容OSX，所以尽量避免使用它的类。</p>
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<p>现在来看看如何计算纹理坐标。第一个方法是将纹理覆盖整个网格，左上角的顶点纹理坐标为(0, 0)，右下角的顶点纹理坐标为(1, 1)。这种方法的问题是，纹理必须是巨大的，以便获得良好的渲染效果，否则纹理将会被过度拉伸。</p>
|
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<p>但我们仍然可以使用非常小的纹理，通过使用高效的技术来获得很好的效果。如果我们设置超出[1, 1]范围的纹理坐标，我们将回到原点并重新开始计算。下图表示在几个正方形中平铺相同的纹理，并超出了[1, 1]范围。</p>
|
||
<p><img alt="纹理坐标I" src="../_static/14/texture_coordinates_i.png" /> </p>
|
||
<p>这是我们在设置纹理坐标时所要做的。我们将一个参数乘以纹理坐标(计算好像整个网格被纹理包裹的情况)，即<code>textInc</code>参数，以增加在相邻顶点之间使用的纹理像素数。</p>
|
||
<p><img alt="纹理坐标II" src="../_static/14/texture_coordinates_ii.png" /> </p>
|
||
<p>目前唯一没有解决的是法线计算。记住我们需要法线，光照才能正确地应用于地形。没有法线，无论光照如何，地形将以相同的颜色渲染。我们在这里使用的方法不一定是最高效的，但它将帮助你理解如何自动计算法线。如果你搜索其他解决方案，可能会发现更有效的方法，只使用相邻点的高度而不需要做交叉相乘操作。尽管如此，这仅需要在启动时完成，这里的方法不会对性能造成太大的损害。</p>
|
||
<p>让我们用图解的方式解释如何计算一个法线值。假设我们有一个名为<strong>P0</strong>的顶点。我们首先计算其周围每个顶点(<strong>P1</strong>, <strong>P2</strong>, <strong>P3</strong>, <strong>P4</strong>)和与连接这些点的面相切的向量。这些向量(<strong>V1</strong>, <strong>V2</strong>, <strong>V3</strong>, <strong>V4</strong>)是通过将每个相邻点与<strong>P0</strong>相减(例如<strong>V1 = P1 - P0</strong>)得到的。</p>
|
||
<p><img alt="法线计算I" src="../_static/14/normals_calc_i.png" /> </p>
|
||
<p>然后，我们计算连接每一个相邻点的平面的法线。这是与之前计算得到的向量交叉相乘计算的。例如，向量<strong>V1</strong>与<strong>V2</strong>所在的平面(蓝色阴影部分)的法线是由<strong>V1</strong>和<strong>V2</strong>交叉相乘得到的，即<strong>V12 = V1 × V2</strong>。</p>
|
||
<p><img alt="法线计算II" src="../_static/14/normals_calc_ii.png" /> </p>
|
||
<p>如果我们计算完毕其他平面的法线(<strong>V23 = V2 × V3</strong>，<strong>V34 = V3 × V4</strong>，<strong>V41 = V4 × V1</strong>)，则法线<strong>P0</strong>就是周围所有平面法线(归一化后)之和：<strong>N0 = V12 + V23 + V34 + V41</strong>。</p>
|
||
<p><img alt="法线计算III" src="../_static/14/normals_calc_iii.png" /></p>
|
||
<p>法线计算的方法实现如下所示。</p>
|
||
<pre><code class="language-java">private float[] calcNormals(float[] posArr, int width, int height) {
|
||
Vector3f v0 = new Vector3f();
|
||
Vector3f v1 = new Vector3f();
|
||
Vector3f v2 = new Vector3f();
|
||
Vector3f v3 = new Vector3f();
|
||
Vector3f v4 = new Vector3f();
|
||
Vector3f v12 = new Vector3f();
|
||
Vector3f v23 = new Vector3f();
|
||
Vector3f v34 = new Vector3f();
|
||
Vector3f v41 = new Vector3f();
|
||
List<Float> normals = new ArrayList<>();
|
||
Vector3f normal = new Vector3f();
|
||
for (int row = 0; row < height; row++) {
|
||
for (int col = 0; col < width; col++) {
|
||
if (row > 0 && row < height -1 && col > 0 && col < width -1) {
|
||
int i0 = row*width*3 + col*3;
|
||
v0.x = posArr[i0];
|
||
v0.y = posArr[i0 + 1];
|
||
v0.z = posArr[i0 + 2];
|
||
|
||
int i1 = row*width*3 + (col-1)*3;
|
||
v1.x = posArr[i1];
|
||
v1.y = posArr[i1 + 1];
|
||
v1.z = posArr[i1 + 2];
|
||
v1 = v1.sub(v0);
|
||
|
||
int i2 = (row+1)*width*3 + col*3;
|
||
v2.x = posArr[i2];
|
||
v2.y = posArr[i2 + 1];
|
||
v2.z = posArr[i2 + 2];
|
||
v2 = v2.sub(v0);
|
||
|
||
int i3 = (row)*width*3 + (col+1)*3;
|
||
v3.x = posArr[i3];
|
||
v3.y = posArr[i3 + 1];
|
||
v3.z = posArr[i3 + 2];
|
||
v3 = v3.sub(v0);
|
||
|
||
int i4 = (row-1)*width*3 + col*3;
|
||
v4.x = posArr[i4];
|
||
v4.y = posArr[i4 + 1];
|
||
v4.z = posArr[i4 + 2];
|
||
v4 = v4.sub(v0);
|
||
|
||
v1.cross(v2, v12);
|
||
v12.normalize();
|
||
|
||
v2.cross(v3, v23);
|
||
v23.normalize();
|
||
|
||
v3.cross(v4, v34);
|
||
v34.normalize();
|
||
|
||
v4.cross(v1, v41);
|
||
v41.normalize();
|
||
|
||
normal = v12.add(v23).add(v34).add(v41);
|
||
normal.normalize();
|
||
} else {
|
||
normal.x = 0;
|
||
normal.y = 1;
|
||
normal.z = 0;
|
||
}
|
||
normal.normalize();
|
||
normals.add(normal.x);
|
||
normals.add(normal.y);
|
||
normals.add(normal.z);
|
||
}
|
||
}
|
||
return Utils.listToArray(normals);
|
||
}
|
||
</code></pre>
|
||
<p>最后，为了创建更大的地形，我们有两个选择：
|
||
* 创建更大的高度图
|
||
* 重用高度图并将其平铺在三维空间中。高度图将像一个地形块，在世界上像瓷砖一样平移。为了做到这一点，高度图边缘的像素必须是相同的(左侧边缘必须与右侧相同，上侧边缘必须与下侧相同)，以避免块之间的间隙。</p>
|
||
<p>我们将使用第二种方法(并选择适当的高度图)。为了做到它，我们将创建一个名为<code>Terrain</code>的类，该类将创建一个正方形的高度图块，定义如下。</p>
|
||
<pre><code class="language-java">package org.lwjglb.engine.items;
|
||
|
||
import org.lwjglb.engine.graph.HeightMapMesh;
|
||
|
||
public class Terrain {
|
||
|
||
private final GameItem[] gameItems;
|
||
|
||
public Terrain(int blocksPerRow, float scale, float minY, float maxY, String heightMap, String textureFile, int textInc) throws Exception {
|
||
gameItems = new GameItem[blocksPerRow * blocksPerRow];
|
||
HeightMapMesh heightMapMesh = new HeightMapMesh(minY, maxY, heightMap, textureFile, textInc);
|
||
for (int row = 0; row < blocksPerRow; row++) {
|
||
for (int col = 0; col < blocksPerRow; col++) {
|
||
float xDisplacement = (col - ((float) blocksPerRow - 1) / (float) 2) * scale * HeightMapMesh.getXLength();
|
||
float zDisplacement = (row - ((float) blocksPerRow - 1) / (float) 2) * scale * HeightMapMesh.getZLength();
|
||
|
||
GameItem terrainBlock = new GameItem(heightMapMesh.getMesh());
|
||
terrainBlock.setScale(scale);
|
||
terrainBlock.setPosition(xDisplacement, 0, zDisplacement);
|
||
gameItems[row * blocksPerRow + col] = terrainBlock;
|
||
}
|
||
}
|
||
}
|
||
|
||
public GameItem[] getGameItems() {
|
||
return gameItems;
|
||
}
|
||
}
|
||
</code></pre>
|
||
<p>让我们详解整个过程，我们拥有由以下坐标定义的块(X和Z使用之前定义的常量)。</p>
|
||
<p><img alt="地形构建I" src="../_static/14/terrain_construction_1.png" /></p>
|
||
<p>假设我们创建了一个由3×3块网格构成的地形。我们假设我们不会缩放地形块(也就是说，变量<code>blocksPerRow</code>是<strong>3</strong>而变量<code>scale</code>将会是<strong>1</strong>)。我们希望网格的中央在坐标系的(0, 0)。</p>
|
||
<p>我们需要移动块，这样顶点就变成如下坐标。</p>
|
||
<p><img alt="地形构建II" src="../_static/14/terrain_construction_2.png" /></p>
|
||
<p>移动是通过调用<code>setPosition</code>方法实现的，但记住，我们所设置的是一个位移而不是一个位置。如果你看到上图，你会发现中央块不需要任何移动，它已经定位在适当的坐标上。绘制绿色顶点需要在X轴上位移<strong>-1</strong>，而绘制蓝色顶点需要在X轴上位移<strong>+1</strong>。计算X位移的公式，要考虑到缩放和块的宽度，公式如下：</p>
|
||
<p>
|
||
<script type="math/tex; mode=display">xDisplacement=(col - (blocksPerRow -1 ) / 2) \times scale \times width</script>
|
||
</p>
|
||
<p>Z位移的公式为：</p>
|
||
<p>
|
||
<script type="math/tex; mode=display">zDisplacement=(row - (blocksPerRow -1 ) / 2) \times scale \times height</script>
|
||
</p>
|
||
<p>如果在<code>DummyGame</code>类中创建一个<code>Terrain</code>实例，我们可以得到如图所示的效果。</p>
|
||
<p><img alt="地形结果" src="../_static/14/terrain_result.png" /> </p>
|
||
<p>你可以在地形周围移动相机，看看它是如何渲染的。由于还没有实现碰撞检测，你可以穿过它并从上面看它。由于我们已经启用了面剔除，当从下面观察时，地形的某些部分不会渲染。</p>
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