java - 如何绘制球体的中半部分(在代码中)

Question

我正在尝试创建一个球体的中半部分。基本上创建一个球体，给出堆栈号和切片号，并且有两个变量 phi (对于切片)和 theta (对于堆栈)负责进度多少。该过程分为创建底盖、主体和顶盖(如下所示)。为了实现中间一半(如下所示中间50%的theta)，我们需要省略大写字母，并以某种方式修改主体。我正在玩弄堆栈号( 1/4*stackNumbers to 3/4*stackNumbers )，但没有给出我想要的结果。

我应该如何修改球体生成以实现中间一半( pi/4 <theta <pi*3/4 )？我的总体问题是如何将球体分成 3 个不同的部分，上部 25%、中部 50% 和底部 25%？ (角度为 25%，即 theta )

以下是以编程方式生成球体的流行代码:

private void generateSphere(int stackNumber, int sliceNumber, boolean facingOut) {
    int capVertexNumber = 3 * sliceNumber;
    int bodyVertexNumber = 4 * sliceNumber * (stackNumber - 2);
    int vertexNumber = (2 * capVertexNumber) + bodyVertexNumber;
    int triangleNumber = (2 * capVertexNumber) + (6 * sliceNumber * (stackNumber - 2));

    vertices = new float[3 * vertexNumber];
    normals = new float[3 * vertexNumber];
    texCoords = new float[2 * vertexNumber];
    indices = new char[triangleNumber];

    // bottom cap
    // createCap(stackNumber, sliceNumber, false, facingOut);

    // body
    createBody(stackNumber, sliceNumber, facingOut);

    // top cap
    createCap(stackNumber, sliceNumber, true, facingOut);
}

private void createCap(int stackNumber, int sliceNumber, boolean top, boolean facingOut) {

    float stackPercentage0;
    float stackPercentage1;

    if (!top) {
        stackPercentage0 = ((float) (stackNumber - 1) / stackNumber);
        stackPercentage1 = 1.0f;

    } else {
        stackPercentage0 = (1.0f / stackNumber);
        stackPercentage1 = 0.0f;
    }

    float t0 = stackPercentage0;
    float t1 = stackPercentage1;
    double theta0 = stackPercentage0 * Math.PI;
    double theta1 = stackPercentage1 * Math.PI;
    double cosTheta0 = Math.cos(theta0);
    double sinTheta0 = Math.sin(theta0);
    double cosTheta1 = Math.cos(theta1);
    double sinTheta1 = Math.sin(theta1);

    for (int slice = 0; slice < sliceNumber; slice++) {
        float slicePercentage0 = ((float) (slice) / sliceNumber);
        float slicePercentage1 = ((float) (slice + 1) / sliceNumber);
        double phi0 = slicePercentage0 * 2.0 * Math.PI;
        double phi1 = slicePercentage1 * 2.0 * Math.PI;
        float s0, s1;
        if (facingOut) {
            s0 = 1 - slicePercentage0;
            s1 = 1 - slicePercentage1;
        } else {
            s0 = slicePercentage0;
            s1 = slicePercentage1;
        }
        float s2 = (s0 + s1) / 2.0f;
        double cosPhi0 = Math.cos(phi0);
        double sinPhi0 = Math.sin(phi0);
        double cosPhi1 = Math.cos(phi1);
        double sinPhi1 = Math.sin(phi1);

        float x0 = (float) (sinTheta0 * cosPhi0);
        float y0 = (float) cosTheta0;
        float z0 = (float) (sinTheta0 * sinPhi0);

        float x1 = (float) (sinTheta0 * cosPhi1);
        float y1 = (float) cosTheta0;
        float z1 = (float) (sinTheta0 * sinPhi1);

        float x2 = (float) (sinTheta1 * cosPhi0);
        float y2 = (float) cosTheta1;
        float z2 = (float) (sinTheta1 * sinPhi0);

        vertices[vertexCount + 0] = x0;
        vertices[vertexCount + 1] = y0;
        vertices[vertexCount + 2] = z0;

        vertices[vertexCount + 3] = x1;
        vertices[vertexCount + 4] = y1;
        vertices[vertexCount + 5] = z1;

        vertices[vertexCount + 6] = x2;
        vertices[vertexCount + 7] = y2;
        vertices[vertexCount + 8] = z2;

        if (facingOut) {
            normals[vertexCount + 0] = x0;
            normals[vertexCount + 1] = y0;
            normals[vertexCount + 2] = z0;

            normals[vertexCount + 3] = x1;
            normals[vertexCount + 4] = y1;
            normals[vertexCount + 5] = z1;

            normals[vertexCount + 6] = x2;
            normals[vertexCount + 7] = y2;
            normals[vertexCount + 8] = z2;
        } else {
            normals[vertexCount + 0] = -x0;
            normals[vertexCount + 1] = -y0;
            normals[vertexCount + 2] = -z0;

            normals[vertexCount + 3] = -x1;
            normals[vertexCount + 4] = -y1;
            normals[vertexCount + 5] = -z1;

            normals[vertexCount + 6] = -x2;
            normals[vertexCount + 7] = -y2;
            normals[vertexCount + 8] = -z2;
        }

        texCoords[texCoordCount + 0] = s0;
        texCoords[texCoordCount + 1] = t0;
        texCoords[texCoordCount + 2] = s1;
        texCoords[texCoordCount + 3] = t0;
        texCoords[texCoordCount + 4] = s2;
        texCoords[texCoordCount + 5] = t1;

        if ((facingOut && top) || (!facingOut && !top)) {
            indices[indexCount + 0] = (char) (triangleCount + 1);
            indices[indexCount + 1] = (char) (triangleCount + 0);
            indices[indexCount + 2] = (char) (triangleCount + 2);
        } else {
            indices[indexCount + 0] = (char) (triangleCount + 0);
            indices[indexCount + 1] = (char) (triangleCount + 1);
            indices[indexCount + 2] = (char) (triangleCount + 2);
        }

        vertexCount += 9;
        texCoordCount += 6;
        indexCount += 3;
        triangleCount += 3;
    }

}

private void createBody(int stackNumber, int sliceNumber, boolean facingOut) {
    for (int stack = 1; stack < stackNumber - 1; stack++) {
        float stackPercentage0 = ((float) (stack) / stackNumber);
        float stackPercentage1 = ((float) (stack + 1) / stackNumber);

        float t0 = stackPercentage0;
        float t1 = stackPercentage1;

        double theta0 = stackPercentage0 * Math.PI;
        double theta1 = stackPercentage1 * Math.PI;
        double cosTheta0 = Math.cos(theta0);
        double sinTheta0 = Math.sin(theta0);
        double cosTheta1 = Math.cos(theta1);
        double sinTheta1 = Math.sin(theta1);

        for (int slice = 0; slice < sliceNumber; slice++) {
            float slicePercentage0 = ((float) (slice) / sliceNumber);
            float slicePercentage1 = ((float) (slice + 1) / sliceNumber);
            double phi0 = slicePercentage0 * 2.0 * Math.PI;
            double phi1 = slicePercentage1 * 2.0 * Math.PI;
            float s0, s1;
            if (facingOut) {
                s0 = 1.0f - slicePercentage0;
                s1 = 1.0f - slicePercentage1;
            } else {
                s0 = slicePercentage0;
                s1 = slicePercentage1;
            }
            double cosPhi0 = Math.cos(phi0);
            double sinPhi0 = Math.sin(phi0);
            double cosPhi1 = Math.cos(phi1);
            double sinPhi1 = Math.sin(phi1);

            float x0 = (float) (sinTheta0 * cosPhi0);
            float y0 = (float) cosTheta0;
            float z0 = (float) (sinTheta0 * sinPhi0);

            float x1 = (float) (sinTheta0 * cosPhi1);
            float y1 = (float) cosTheta0;
            float z1 = (float) (sinTheta0 * sinPhi1);

            float x2 = (float) (sinTheta1 * cosPhi0);
            float y2 = (float) cosTheta1;
            float z2 = (float) (sinTheta1 * sinPhi0);

            float x3 = (float) (sinTheta1 * cosPhi1);
            float y3 = (float) cosTheta1;
            float z3 = (float) (sinTheta1 * sinPhi1);

            vertices[vertexCount + 0] = x0;
            vertices[vertexCount + 1] = y0;
            vertices[vertexCount + 2] = z0;

            vertices[vertexCount + 3] = x1;
            vertices[vertexCount + 4] = y1;
            vertices[vertexCount + 5] = z1;

            vertices[vertexCount + 6] = x2;
            vertices[vertexCount + 7] = y2;
            vertices[vertexCount + 8] = z2;

            vertices[vertexCount + 9] = x3;
            vertices[vertexCount + 10] = y3;
            vertices[vertexCount + 11] = z3;

            if (facingOut) {
                normals[vertexCount + 0] = x0;
                normals[vertexCount + 1] = y0;
                normals[vertexCount + 2] = z0;

                normals[vertexCount + 3] = x1;
                normals[vertexCount + 4] = y1;
                normals[vertexCount + 5] = z1;

                normals[vertexCount + 6] = x2;
                normals[vertexCount + 7] = y2;
                normals[vertexCount + 8] = z2;

                normals[vertexCount + 9] = x3;
                normals[vertexCount + 10] = y3;
                normals[vertexCount + 11] = z3;
            } else {
                normals[vertexCount + 0] = -x0;
                normals[vertexCount + 1] = -y0;
                normals[vertexCount + 2] = -z0;

                normals[vertexCount + 3] = -x1;
                normals[vertexCount + 4] = -y1;
                normals[vertexCount + 5] = -z1;

                normals[vertexCount + 6] = -x2;
                normals[vertexCount + 7] = -y2;
                normals[vertexCount + 8] = -z2;

                normals[vertexCount + 9] = -x3;
                normals[vertexCount + 10] = -y3;
                normals[vertexCount + 11] = -z3;
            }

            texCoords[texCoordCount + 0] = s0;
            texCoords[texCoordCount + 1] = t0;
            texCoords[texCoordCount + 2] = s1;
            texCoords[texCoordCount + 3] = t0;
            texCoords[texCoordCount + 4] = s0;
            texCoords[texCoordCount + 5] = t1;
            texCoords[texCoordCount + 6] = s1;
            texCoords[texCoordCount + 7] = t1;

            // one quad looking from outside toward center
            //
            // @formatter:off
            //
            // s1 --> s0
            //
            // t0 1-----0
            // | | |
            // v | |
            // t1 3-----2
            //
            // @formatter:on
            //
            // Note that tex_coord t increase from top to bottom because the
            // texture image is loaded upside down.
            if (facingOut) {
                indices[indexCount + 0] = (char) (triangleCount + 0);
                indices[indexCount + 1] = (char) (triangleCount + 1);
                indices[indexCount + 2] = (char) (triangleCount + 2);

                indices[indexCount + 3] = (char) (triangleCount + 2);
                indices[indexCount + 4] = (char) (triangleCount + 1);
                indices[indexCount + 5] = (char) (triangleCount + 3);
            } else {
                indices[indexCount + 0] = (char) (triangleCount + 0);
                indices[indexCount + 1] = (char) (triangleCount + 2);
                indices[indexCount + 2] = (char) (triangleCount + 1);

                indices[indexCount + 3] = (char) (triangleCount + 2);
                indices[indexCount + 4] = (char) (triangleCount + 3);
                indices[indexCount + 5] = (char) (triangleCount + 1);
            }

            vertexCount += 12;
            texCoordCount += 8;
            indexCount += 6;
            triangleCount += 4;
        }
    }

} 

Answer 1

这里的代码使用 spherical coordinates来计算球体。 theta 是代表您感兴趣的上/下坐标的变量，theta 从 0 到 PI。您想从 PI/4 转到 3PI/4。 stackNumbers 只是表示球体中的划分数，因为您可以看到它用作 stack 的分母，这是要更改的错误变量。因此，您可以对代码进行以下更改。来自:

double theta0 = stackPercentage0 * Math.PI;
double theta1 = stackPercentage1 * Math.PI;

至:

double startTheta = Math.PI / 4;
double endTheta = 3 * Math.PI / 4;
double theta0 = stackPercentage0 * (endTheta - startTheta) + startTheta;
double theta1 = stackPercentage1 * (endTheta - startTheta) + startTheta;

由于您没有使用上限，因此您需要更改开始和结束堆栈编号以反射(reflect)这一点:

for (int stack = 1; stack < stackNumber - 1; stack++) { // old
for (int stack = 0; stack < stackNumber; stack++) { // new

此外，由于您现在有更多的 body 面孔，因此您需要为它们更新适当的容器。将 (stackNumber - 2) 替换为 (stackNumber - 1)。