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如何将 SuperShape3D 绘制为网格？

发布于 2024-10-14 17:42:25 字数 4001 浏览 3 评论 0原文

我想绘制一个 3D Superformula 网格，但不知道应该如何组织面（是它们是三角形或四边形）。

我已经安装了八度并尝试了示例代码。我不知道 Gnuplot 的 mesh() 函数是如何工作的，但我想我需要类似的东西。

维基百科条目有一个指向处理演示的链接。 我查看了来源，发现它只得出点。 我试图将这段代码包装在 beginShape()/endShape() 中 打电话，但按我希望的方式工作。

我还尝试检查点数是否可以被 3 整除 或 4 并使用三角形或四边形，但这不是正确的方法， 如下所示： SuperShape Processing

如何使用三角形/四边形绘制 SuperShape3D？ 我想象顶点位于正确的位置，但它们 需要对使用绘制脸部的调用进行排序 顶点索引。

我目前还没有固定使用某种特定的语言，但是 我的目标是将顶点放在数组中，然后 使用顶点索引推面（3 或 4 点）。

有什么提示吗？

更新：

这是用于获取处理示例代码中的点的函数：

import toxi.geom.*;
import controlP5.*;

ControlP5 controlP5;
ArrayList points = new ArrayList();
ArrayList faces = new ArrayList();

float a1=1,a2=1,b=1,xx,step = 0.05,yy,zz,n1=4,n2=12,n3=15,n4=15,r,raux1,r1,raux2,r2;
int N_X = int(2*PI/step);
int N_Y = int(PI/step);


void setup() {
  size(800,800,P3D);
  //hint(ENABLE_DEPTH_SORT);

  controlP5 = new ControlP5(this);

  controlP5.addSlider("a1value",0,3,1,20,0,200,10);
  controlP5.addSlider("a2value",0,3,1,20,20,200,10);
  controlP5.addSlider("bvalue",0,3,1,20,40,200,10);
  controlP5.addSlider("n1value",0,20,8,20,60,200,10);
  controlP5.addSlider("n2value",0,5,0.5,20,80,200,10);
  controlP5.addSlider("n3value",0,5,0.5,20,100,200,10);
  controlP5.addSlider("n4value",0,20,8,20,120,200,10);
  controlP5.addSlider("stepvalue",0.02,0.9,0.05,20,140,200,10);
  controlP5.setAutoDraw(false);
  draw_super_formula();
}

void draw() {
  background(0);
  fill(255);
  controlP5.draw();
  lights();
  translate(width / 2, height / 2, 0);
  rotateX(mouseY * 0.01f);
  rotateY(mouseX * 0.01f);
  // connect 4 points into quads:
  Vec3D pt;
  for(int x=0;x<N_X-1;x++)
  {
    for(int y=0;y<N_Y-1;y++)
    {
      beginShape(QUADS);
      pt = (Vec3D)points.get( x*N_Y + y );
      vertex(pt.x,pt.y,pt.z);
      pt = (Vec3D)points.get( x*N_Y + y+1 );
      vertex(pt.x,pt.y,pt.z);
      pt = (Vec3D)points.get( (x+1)*N_Y + y+1 );
      vertex(pt.x,pt.y,pt.z);
      pt = (Vec3D)points.get( (x+1)*N_Y + y);
      vertex(pt.x,pt.y,pt.z);
      endShape();
    }
  }
}

void vertex(Vec3D v) {
  vertex(v.x,v.y,v.z);
}

void draw_super_formula() {
  for(int i = points.size()-1; i>0;i--){
    points.remove(i);
  }

  for(int x=0;x<N_X;x++)
  {
    float i = -PI + x*step;
    for(int y=0;y<N_Y;y++)
    {
      float j = -PI/2.0 + y*step;
      raux1=pow(abs(1/a1*abs(cos(n1*i/4))),n3)+pow(abs(1/a2*abs(sin(n1*i/4))),n4);
      r1=pow(abs(raux1),(-1/n2));
      raux2=pow(abs(1/a1*abs(cos(n1*j/4))),n3)+pow(abs(1/a2*abs(sin(n1*j/4))),n4);
      r2=pow(abs(raux2),(-1/n2));
      xx=r1*cos(i)*r2*cos(j)*100;
      yy=r1*sin(i)*r2*cos(j)*100;
      zz=r2*sin(j)*100;

      Vec3D test1 = new Vec3D(xx,yy,zz);
      points.add(test1);
    }
  }
}

void bvalue(float new_value){
  b = new_value;
  draw_super_formula();
}
void a1value(float new_value){
  a1 = new_value;
  draw_super_formula();
}
void a2value(float new_value){
  a2 = new_value;
  draw_super_formula();
}
void n1value(float new_value){
  n1 = new_value;
  draw_super_formula();
}
void n2value(float new_value){
  n2 = new_value;
  draw_super_formula();
}
void n3value(float new_value){
  n3 = new_value;
  draw_super_formula();
}
void n4value(float new_value){
  n4 = new_value;
  draw_super_formula();
}

void stepvalue(float new_value){
  step = new_value;
  draw_super_formula();
  println("% 3: "+(points.size()%3));
  println("% 4: "+(points.size()%4));
}
class F4{
  int a,b,c,d;
  F4(int a,int b,int c,int d){
    this.a = a;
    this.b = b;
    this.c = c;
    this.d = d;
  }
}

@tim_hutton 的解决方案很棒，但它看起来索引关闭，试图找出它在哪里。

superformula 问题

原文

I would like to draw a 3D Superformula mesh but not sure how I should organize the faces(be them triangles or quads).

I've installed octave and tried the sample code. I have no clue how Gnuplot's mesh() function works, but I imagine I would need something similar.

The Wikipedia entry has a link to a Processing demo.
I had a look at the source and noticed it only draws points.
I tried to wrap that segment of code within beginShape()/endShape()
calls but work the way I hoped.

I also tried to check if the number of points is divisible by 3
or 4 and used TRIANGLES or QUADS, but this is not the right way to do this,
as you can see below:
SuperShape Processing

How can I draw a SuperShape3D using triangles/quads ?
I imagine the vertices are in the right positions, but they
need to be sorted to calls that would draw the faces using
the vertex indices.

I'm not fixed to a particular language at the moment, but
my goal would be to have the vertices in an array, then
push faces(3 or 4 points) using vertex indices.

Any hints ?

Update:

Here is the function used to get the points in the Processing sample code:

import toxi.geom.*;
import controlP5.*;

ControlP5 controlP5;
ArrayList points = new ArrayList();
ArrayList faces = new ArrayList();

float a1=1,a2=1,b=1,xx,step = 0.05,yy,zz,n1=4,n2=12,n3=15,n4=15,r,raux1,r1,raux2,r2;
int N_X = int(2*PI/step);
int N_Y = int(PI/step);


void setup() {
  size(800,800,P3D);
  //hint(ENABLE_DEPTH_SORT);

  controlP5 = new ControlP5(this);

  controlP5.addSlider("a1value",0,3,1,20,0,200,10);
  controlP5.addSlider("a2value",0,3,1,20,20,200,10);
  controlP5.addSlider("bvalue",0,3,1,20,40,200,10);
  controlP5.addSlider("n1value",0,20,8,20,60,200,10);
  controlP5.addSlider("n2value",0,5,0.5,20,80,200,10);
  controlP5.addSlider("n3value",0,5,0.5,20,100,200,10);
  controlP5.addSlider("n4value",0,20,8,20,120,200,10);
  controlP5.addSlider("stepvalue",0.02,0.9,0.05,20,140,200,10);
  controlP5.setAutoDraw(false);
  draw_super_formula();
}

void draw() {
  background(0);
  fill(255);
  controlP5.draw();
  lights();
  translate(width / 2, height / 2, 0);
  rotateX(mouseY * 0.01f);
  rotateY(mouseX * 0.01f);
  // connect 4 points into quads:
  Vec3D pt;
  for(int x=0;x<N_X-1;x++)
  {
    for(int y=0;y<N_Y-1;y++)
    {
      beginShape(QUADS);
      pt = (Vec3D)points.get( x*N_Y + y );
      vertex(pt.x,pt.y,pt.z);
      pt = (Vec3D)points.get( x*N_Y + y+1 );
      vertex(pt.x,pt.y,pt.z);
      pt = (Vec3D)points.get( (x+1)*N_Y + y+1 );
      vertex(pt.x,pt.y,pt.z);
      pt = (Vec3D)points.get( (x+1)*N_Y + y);
      vertex(pt.x,pt.y,pt.z);
      endShape();
    }
  }
}

void vertex(Vec3D v) {
  vertex(v.x,v.y,v.z);
}

void draw_super_formula() {
  for(int i = points.size()-1; i>0;i--){
    points.remove(i);
  }

  for(int x=0;x<N_X;x++)
  {
    float i = -PI + x*step;
    for(int y=0;y<N_Y;y++)
    {
      float j = -PI/2.0 + y*step;
      raux1=pow(abs(1/a1*abs(cos(n1*i/4))),n3)+pow(abs(1/a2*abs(sin(n1*i/4))),n4);
      r1=pow(abs(raux1),(-1/n2));
      raux2=pow(abs(1/a1*abs(cos(n1*j/4))),n3)+pow(abs(1/a2*abs(sin(n1*j/4))),n4);
      r2=pow(abs(raux2),(-1/n2));
      xx=r1*cos(i)*r2*cos(j)*100;
      yy=r1*sin(i)*r2*cos(j)*100;
      zz=r2*sin(j)*100;

      Vec3D test1 = new Vec3D(xx,yy,zz);
      points.add(test1);
    }
  }
}

void bvalue(float new_value){
  b = new_value;
  draw_super_formula();
}
void a1value(float new_value){
  a1 = new_value;
  draw_super_formula();
}
void a2value(float new_value){
  a2 = new_value;
  draw_super_formula();
}
void n1value(float new_value){
  n1 = new_value;
  draw_super_formula();
}
void n2value(float new_value){
  n2 = new_value;
  draw_super_formula();
}
void n3value(float new_value){
  n3 = new_value;
  draw_super_formula();
}
void n4value(float new_value){
  n4 = new_value;
  draw_super_formula();
}

void stepvalue(float new_value){
  step = new_value;
  draw_super_formula();
  println("% 3: "+(points.size()%3));
  println("% 4: "+(points.size()%4));
}
class F4{
  int a,b,c,d;
  F4(int a,int b,int c,int d){
    this.a = a;
    this.b = b;
    this.c = c;
    this.d = d;
  }
}

@tim_hutton's solution is great, but it looks an index off, trying to figure out where that is.

superformula issue

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评论（1）

霞映澄塘 2024-10-21 17:42:25

超级公式为您提供每个采样角度的半径。在 3D 中，您需要两个角度：theta 和 phi。通过保持 theta 固定并改变 phi（反之亦然），您将沿着一个大圆进行采样。

制作曲面的一种方法是通过根据角度 a 和 b 采样四个点来制作四边形：(a,b)、(a+da,b)、(a+da,b+db)、(a,b) +db）。对 a: 0,da,2*da... 和 b: 0,db,2*db... 执行此操作，直到覆盖整个表面。使用小 da 和 db 得到小四边形。

（另一种方法是使用通用表面重建算法 (1,2）但这对于这样的问题来说有点过分了。）

更新：

我认为代码下面是你想要的东西：


import toxi.geom.*;
import controlP5.*;

ControlP5 controlP5;
ArrayList points = new ArrayList();
ArrayList faces = new ArrayList();

float a1=1,a2=1,b=1,xx,step = 0.05,yy,zz,n1=4,n2=12,n3=15,n4=15,r,raux1,r1,raux2,r2;
int N_X = int(2*PI/step);
int N_Y = int(PI/step);


void setup() {
  size(800,800,P3D);
  //hint(ENABLE_DEPTH_SORT);

  controlP5 = new ControlP5(this);

  controlP5.addSlider("a1value",0,3,1,20,0,200,10);
  controlP5.addSlider("a2value",0,3,1,20,20,200,10);
  controlP5.addSlider("bvalue",0,3,1,20,40,200,10);
  controlP5.addSlider("n1value",0,20,8,20,60,200,10);
  controlP5.addSlider("n2value",0,5,0.5,20,80,200,10);
  controlP5.addSlider("n3value",0,5,0.5,20,100,200,10);
  controlP5.addSlider("n4value",0,20,8,20,120,200,10);
  controlP5.addSlider("stepvalue",0.02,0.9,0.05,20,140,200,10);
  controlP5.setAutoDraw(false);
  draw_super_formula();
}

void draw() {
  background(0);
  fill(255);

  controlP5.draw();

  translate(width / 2, height / 2, 0);
  rotateX(mouseY * 0.01f);
  rotateY(mouseX * 0.01f);
  drawAxes(300);
  beginShape(POINTS);
  for(int i = 0; i < points.size();i++){
    Vec3D k = (Vec3D)points.get(i); 
    stroke(color(k.x+110,k.y+110,k.z+110));
    vertex(k.x,k.y,k.z);
  }
  endShape();

  // connect 4 points into quads:
  Vec3D pt;
  noFill();
  for(int x=0;x<N_X-1;x++)
  {
    for(int y=0;y<N_Y-1;y++)
    {
      beginShape();
      pt = (Vec3D)points.get( x*N_Y + y );
      vertex(pt.x,pt.y,pt.z);
      pt = (Vec3D)points.get( x*N_Y + y+1 );
      vertex(pt.x,pt.y,pt.z);
      pt = (Vec3D)points.get( (x+1)*N_Y + y+1 );
      vertex(pt.x,pt.y,pt.z);
      pt = (Vec3D)points.get( (x+1)*N_Y + y);
      vertex(pt.x,pt.y,pt.z);
      endShape();
    }
  }
}

void vertex(Vec3D v) {
  vertex(v.x,v.y,v.z);
}

void draw_super_formula() {
  for(int i = points.size()-1; i>0;i--){
    points.remove(i);
  }

  for(int x=0;x<N_X;x++)
  {
    float i = -PI + x*step;
    for(int y=0;y<N_Y;y++)
    {
      float j = -PI/2.0 + y*step;
      raux1=pow(abs(1/a1*abs(cos(n1*i/4))),n3)+pow(abs(1/a2*abs(sin(n1*i/4))),n4);
      r1=pow(abs(raux1),(-1/n2));
      raux2=pow(abs(1/a1*abs(cos(n1*j/4))),n3)+pow(abs(1/a2*abs(sin(n1*j/4))),n4);
      r2=pow(abs(raux2),(-1/n2));
      xx=r1*cos(i)*r2*cos(j)*100;
      yy=r1*sin(i)*r2*cos(j)*100;
      zz=r2*sin(j)*100;

      Vec3D test1 = new Vec3D(xx,yy,zz);
      points.add(test1);
    }
  }
}

void drawAxes(float l) {
  stroke(255, 0, 0);
  line(0, 0, 0, l, 0, 0);
  line(l, 0, 0, l-10, 10, 0);
  line(l, 0, 0, l-10, -10, 0);

  stroke(0, 255, 0);
  line(0, 0, 0, 0, l, 0);
  line(0, l, 0, 10, l-10, 0);
  line(0, l, 0, -10, l-10, 0);

  stroke(0, 0, 255);

  line(0, 0, 0, 0, 0, l);
  line(0, 0, l, 0, 10, l-10);
  line(0, 0, l, 0, -10, l-10);

}

void bvalue(float new_value){
  b = new_value;
  draw_super_formula();
}
void a1value(float new_value){
  a1 = new_value;
  draw_super_formula();
}
void a2value(float new_value){
  a2 = new_value;
  draw_super_formula();
}
void n1value(float new_value){
  n1 = new_value;
  draw_super_formula();
}
void n2value(float new_value){
  n2 = new_value;
  draw_super_formula();
}
void n3value(float new_value){
  n3 = new_value;
  draw_super_formula();
}
void n4value(float new_value){
  n4 = new_value;
  draw_super_formula();
}

void stepvalue(float new_value){
  step = new_value;
  draw_super_formula();
  println("% 3: "+(points.size()%3));
  println("% 4: "+(points.size()%4));
}
class F4{
  int a,b,c,d;
  F4(int a,int b,int c,int d){
    this.a = a;
    this.b = b;
    this.c = c;
    this.d = d;
  }
}

The superformula gives you a radius for each angle sampled. In 3D you need two angles: theta and phi. By keeping theta fixed and varying phi (or vice versa) you will sample along a great circle.

One way to make a surface is to make quads by sampling four points based on the angles a and b: (a,b), (a+da,b), (a+da,b+db), (a,b+db). Do this for a: 0,da,2*da... and for b: 0,db,2*db... until the whole surface is covered. Use a small da and db to get small quads.

(The alternative is to use a generic surface reconstruction algorithm (1,2) but this is overkill for a problem like this.)

Update:

I think the code below is something like what you want:


import toxi.geom.*;
import controlP5.*;

ControlP5 controlP5;
ArrayList points = new ArrayList();
ArrayList faces = new ArrayList();

float a1=1,a2=1,b=1,xx,step = 0.05,yy,zz,n1=4,n2=12,n3=15,n4=15,r,raux1,r1,raux2,r2;
int N_X = int(2*PI/step);
int N_Y = int(PI/step);


void setup() {
  size(800,800,P3D);
  //hint(ENABLE_DEPTH_SORT);

  controlP5 = new ControlP5(this);

  controlP5.addSlider("a1value",0,3,1,20,0,200,10);
  controlP5.addSlider("a2value",0,3,1,20,20,200,10);
  controlP5.addSlider("bvalue",0,3,1,20,40,200,10);
  controlP5.addSlider("n1value",0,20,8,20,60,200,10);
  controlP5.addSlider("n2value",0,5,0.5,20,80,200,10);
  controlP5.addSlider("n3value",0,5,0.5,20,100,200,10);
  controlP5.addSlider("n4value",0,20,8,20,120,200,10);
  controlP5.addSlider("stepvalue",0.02,0.9,0.05,20,140,200,10);
  controlP5.setAutoDraw(false);
  draw_super_formula();
}

void draw() {
  background(0);
  fill(255);

  controlP5.draw();

  translate(width / 2, height / 2, 0);
  rotateX(mouseY * 0.01f);
  rotateY(mouseX * 0.01f);
  drawAxes(300);
  beginShape(POINTS);
  for(int i = 0; i < points.size();i++){
    Vec3D k = (Vec3D)points.get(i); 
    stroke(color(k.x+110,k.y+110,k.z+110));
    vertex(k.x,k.y,k.z);
  }
  endShape();

  // connect 4 points into quads:
  Vec3D pt;
  noFill();
  for(int x=0;x<N_X-1;x++)
  {
    for(int y=0;y<N_Y-1;y++)
    {
      beginShape();
      pt = (Vec3D)points.get( x*N_Y + y );
      vertex(pt.x,pt.y,pt.z);
      pt = (Vec3D)points.get( x*N_Y + y+1 );
      vertex(pt.x,pt.y,pt.z);
      pt = (Vec3D)points.get( (x+1)*N_Y + y+1 );
      vertex(pt.x,pt.y,pt.z);
      pt = (Vec3D)points.get( (x+1)*N_Y + y);
      vertex(pt.x,pt.y,pt.z);
      endShape();
    }
  }
}

void vertex(Vec3D v) {
  vertex(v.x,v.y,v.z);
}

void draw_super_formula() {
  for(int i = points.size()-1; i>0;i--){
    points.remove(i);
  }

  for(int x=0;x<N_X;x++)
  {
    float i = -PI + x*step;
    for(int y=0;y<N_Y;y++)
    {
      float j = -PI/2.0 + y*step;
      raux1=pow(abs(1/a1*abs(cos(n1*i/4))),n3)+pow(abs(1/a2*abs(sin(n1*i/4))),n4);
      r1=pow(abs(raux1),(-1/n2));
      raux2=pow(abs(1/a1*abs(cos(n1*j/4))),n3)+pow(abs(1/a2*abs(sin(n1*j/4))),n4);
      r2=pow(abs(raux2),(-1/n2));
      xx=r1*cos(i)*r2*cos(j)*100;
      yy=r1*sin(i)*r2*cos(j)*100;
      zz=r2*sin(j)*100;

      Vec3D test1 = new Vec3D(xx,yy,zz);
      points.add(test1);
    }
  }
}

void drawAxes(float l) {
  stroke(255, 0, 0);
  line(0, 0, 0, l, 0, 0);
  line(l, 0, 0, l-10, 10, 0);
  line(l, 0, 0, l-10, -10, 0);

  stroke(0, 255, 0);
  line(0, 0, 0, 0, l, 0);
  line(0, l, 0, 10, l-10, 0);
  line(0, l, 0, -10, l-10, 0);

  stroke(0, 0, 255);

  line(0, 0, 0, 0, 0, l);
  line(0, 0, l, 0, 10, l-10);
  line(0, 0, l, 0, -10, l-10);

}

void bvalue(float new_value){
  b = new_value;
  draw_super_formula();
}
void a1value(float new_value){
  a1 = new_value;
  draw_super_formula();
}
void a2value(float new_value){
  a2 = new_value;
  draw_super_formula();
}
void n1value(float new_value){
  n1 = new_value;
  draw_super_formula();
}
void n2value(float new_value){
  n2 = new_value;
  draw_super_formula();
}
void n3value(float new_value){
  n3 = new_value;
  draw_super_formula();
}
void n4value(float new_value){
  n4 = new_value;
  draw_super_formula();
}

void stepvalue(float new_value){
  step = new_value;
  draw_super_formula();
  println("% 3: "+(points.size()%3));
  println("% 4: "+(points.size()%4));
}
class F4{
  int a,b,c,d;
  F4(int a,int b,int c,int d){
    this.a = a;
    this.b = b;
    this.c = c;
    this.d = d;
  }
}
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