如何绘制球体的中间部分(在代码中) [英] How to draw the middle half of a sphere (in code)
问题描述
我正在尝试创建一个球体的中间部分.基本上，要创建一个球体，将给出堆栈编号和切片编号，并且有两个变量phi(用于切片)和theta(用于堆栈)负责进度.然后将过程分为创建底盖，主体和顶盖(如下所示).要达到中间一半(如下所示为中间50％的theta)，我们需要省略盖帽，并以某种方式修改主体.我在玩堆栈号(1/4*stackNumbers to 3/4*stackNumbers)，但没有给出我想要的结果.
I'm trying to create the middle half of a sphere. Basically to create a sphere, stack numbers and slice numbers are given, and there are two variables phi (for slices) and theta (for stacks) responsible for how much to progress. And the process is divided into creating bottom cap, body, and top cap (as seen below). To achieve middle half (theta of middle 50% as below), we need to omit the caps, and somehow modify the body. I was playing around with stack numbers (1/4*stackNumbers to 3/4*stackNumbers) but didn't give the result I wanted.
如何修改球体生成以达到中间一半( pi/4 <theta <pi*3/4 )?我的总体问题是如何将球体分成上25％，中50％和下25％的3个不同部分? (以角度计，即theta的25％)
How should I modify the sphere generation to achieve the middle half (pi/4 <theta <pi*3/4)? My overall problem is how can I split the sphere into 3 different parts upper 25%, middle 50%, and bottom 25%? (25% in terms of angle, i.e. theta)
以下是流行的以编程方式生成球体的代码:
Here is the popular code for generating a sphere programmatically:
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;
}
}
}
推荐答案
此处的代码使用球坐标计算球体. 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仅表示球体中的分割数，因为您可以看到它用作堆栈的分母，这是更改错误的变量.因此，您可以对代码进行以下更改.发件人:
The code here is using spherical coordinates to calculate the sphere. theta is the variable that represents the up/down coordinate that you're interested in, and theta goes from 0 to PI. You want to go from PI/4 to 3PI/4. stackNumbers simply represent the number of divisions in the sphere, since you can see that it is used as a denominator for stack, which is the wrong variable to change. So you can make the following changes to the code instead. From:
double theta0 = stackPercentage0 * Math.PI;
double theta1 = stackPercentage1 * Math.PI;
收件人:
double startTheta = Math.PI / 4;
double endTheta = 3 * Math.PI / 4;
double theta0 = stackPercentage0 * (endTheta - startTheta) + startTheta;
double theta1 = stackPercentage1 * (endTheta - startTheta) + startTheta;
由于您没有使用大写字母，因此需要更改起始和结束堆栈编号以反映这一点:
And since you aren't using the caps you need to change the start and end stack numbers to reflect that:
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身体面孔，因此您需要为它们更新适当的容器.将(stackNumber - 2)替换为(stackNumber - 1).
Also, you because you have more body faces now, you need to update the appropriate container for them. Replace (stackNumber - 2) with (stackNumber - 1).
这篇关于如何绘制球体的中间部分(在代码中)的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！
