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在一个相关问题中,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。现在这是可行的,但是我试图通过这些点绘制的圆锥曲线(在这种情况下为抛物线)并未绘制。

我认为元素“圆锥”的构造函数可能对给定点的定义方式很挑剔,所以我最终添加了属性“子对象”,这些点是在绘制圆锥时可以引用的点。

在我下面的代码中,构造函数PPoint创建了具有各自属性pcoord的对象,这是使用原生 jsxgraph 构造函数为点创建的“点”类型的几何对象。pcoord是在调用方法“draw”来绘制点 I_1-I-4 和 p_1 时分配的。

在代码的最后几行中,应该参考对象 I_1-I_4 和 p_1 的 pcoord 来绘制抛物线但由于某种原因没有绘制抛物线。

这怎么可能解决?链接到 jsfiddle。调试时代码在没有错误通知的情况下执行。

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
4

1 回答 1

1

这段代码有两个问题:

1) 在PPoint.draw参考文献 2 中 JSXGraph 点不起作用:在每次更新中都会创建一个新的 JSXGraph 点。这使得代码变慢并且 - 此外 - 不会影响提供给圆锥曲线部分的初始点。我建议改为draw

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)。这是起始值的情况omega = 0

这是一个工作示例:https ://jsfiddle.net/L2d4zt8q/

于 2019-05-25T12:04:24.400 回答