Question

在related question中，我正在寻找一种在3D空间中绘制点的方法，以便这些点将根据滑块值移动。现在可以正常工作了，但是我试图通过这些点绘制的圆锥截面（在这种情况下为抛物线形）并未绘制。

我认为元素“圆锥形”的构造函数可能对如何定义给定点有些挑剔，因此我最终添加了“子对象”作为属性，这些子对象是绘制圆锥形时可以引用的点。

在下面的代码中，构造函数 PPoint 创建具有各自属性 pcoord 的对象，这是使用本机jsxgraph创建的“点”类型的几何对象点的构造函数。当调用“绘制”方法将绘制点I_1-I-4和p_1时分配给 pcoord 。

在代码的最后几行中，应通过引用对象I_1-I_4和p_1的 pcoord 来绘制抛物线，但由于某些原因，未绘制抛物线。

如何解决？ Link to jsfiddle。调试时，执行代码时不会发出错误通知。

HTML

<div id="jxgbox" class="jxgbox" style="width:500px; height:500px">
</div>

JS

const board = JXG.JSXGraph.initBoard('jxgbox', {
  boundingbox: [-10, 10, 10, -10],
  axis: true,
  showCopyright: true,
  showNavigation: true,
  pan: false,
  grid: false,

  zoom: {
    factorX: 1.25,
    factorY: 1.25,
    wheel: false
  }
});

//create z axis
var zAxis = board.create('axis', [
  [0, 0],
  [-1, -1]
], {
  ticks: {
    majorHeight: 10,
    drawLabels: false
  }
});

//create direction of view for projections
var cam = [4, 4, 30]; // [x,y,z]
var r = 6.0;
var origin = [0, 0, 0];

// Function for parallel projection
var project = function(crd, cam) {
  var d = -crd[2] / cam[2];
  return [1, crd[0] + d * cam[0], crd[1] + d * cam[1]];
};

//create slider for rotating the parabola
var sRadius = board.create('slider', [
  [1, -8.5],
  [6, -8.5],
  [-10, 0, 10]
], {
  name: 'angle',
  needsRegularUpdate: true
  //snapWidth: 1
});

//create slider for adjusting the angular speed
var sOmega = board.create('slider', [
  [1, -7.5],
  [6, -7.5],
  [0, 0, 10]
], {
  name: 'Omega',
  needsRegularUpdate: true
  //snapWidth: 1,
});

//fix parameters
const g = 9.81 //gravitational acceleration
const h0 = 5 //initial height of the water surface

//define radius from the y-axis for I3 and I4
const R34 = Math.sqrt(2);


// Function for parallel projection
var project = function(crd, cam) {
  var d = -crd[2] / cam[2];
  return [1, crd[0] + d * cam[0], crd[1] + d * cam[1]];
};


//function creates points for drawing conic sections
function PPoint(radius, sign, namep, fixval) {
  this.R = radius;
  this.S = sign;
  this.Namep = namep;
  this.Fixval = fixval;
  this.pcoord = undefined; //Cartesian coordinates of the point, stored as a point
}

//method for drawing each Point
PPoint.prototype.draw = function(pp) {
  board.create('point', [function() {
    var K1 = sOmega.Value() * sOmega.Value() / g,
      KK = 1 / 4 * sOmega.Value() * sOmega.Value() / g,
      v = sRadius.Value() * Math.PI * 0.5 / 10.0,
      c = [pp.S * pp.R * Math.sin(v), K1 / 2 * pp.R * pp.R - KK + h0, pp.S * pp.R * Math.cos(v)];
    //store the dynamically assigned coordinates of the point for drawing the parabola
    pp.pcoord = board.create('point', [function() {
      return project(c, cam);
    }], {
        visible: false
        }); //end storing pp.coord
    return project(c, cam);
  }], {
    fixed: this.Fixval,
    name: this.Namep,
    visible: true
  })
}


//create and draw points
var p_1 = new PPoint(0, -1, 'p_1', 'false');
var I_1 = new PPoint(r, 1, 'I_1', 'false');
var I_2 = new PPoint(r, -1, 'I_2', 'false');
var I_3 = new PPoint(R34, 1, 'I_3', 'false');
var I_4 = new PPoint(R34, -1, 'I_4', 'false');
p_1.draw(p_1)
I_1.draw(I_1)
I_2.draw(I_2)
I_3.draw(I_3)
I_4.draw(I_4)



//draw the rotating parabola
var prbl = board.create('conic', [I_1.pcoord, I_2.pcoord, I_3.pcoord, I_4.pcoord, p_1.pcoord], {
  strokeColor: '#CA7291',
  strokeWidth: 2,
  trace :true
});

//debugger

Answer 1

此代码有两个问题：

1）在PPoint.draw中，引用两个JSXGraph点不起作用：在每次更新中，都会创建一个新的JSXGraph点。这使代码变慢，而且-不影响提供给圆锥部分的初始点。我建议将draw更改为此：

PPoint.prototype.draw = function(pp) {
  pp.pcoord = board.create('point', [function() {
    var K1 = sOmega.Value() * sOmega.Value() / g,
      KK = 1 / 4 * sOmega.Value() * sOmega.Value() / g,
      v = sRadius.Value() * Math.PI * 0.5 / 10.0,
      c = [pp.S * pp.R * Math.sin(v), 
           K1 / 2 * pp.R * pp.R - KK + h0, 
           pp.S * pp.R * Math.cos(v)];
      return project(c, cam);
  }], {
    fixed: this.Fixval,
    name: this.Namep,
    visible: true});

2）第二个问题是JSXGraph无法通过五个点绘制退化的圆锥曲线，并且如果圆锥曲线接近退化，则精度会受到影响（一般抛物线存在数值问题）。起始值omega = 0在这里就是这种情况。

这是一个有效的示例：https://jsfiddle.net/L2d4zt8q/

在jsxgraph中，为什么没有在同一平面上通过五个点绘制抛物线？

1 个答案: