Three.js Object3d 圆柱体旋转以对齐向量

Question

我进行了广泛的搜索，但似乎无法弄清楚这个非常基本的事情。一两年前，我在 stackoverflow 和其他地方看到过其他示例，但它们无法与最新版本的 Three.js 一起使用。

这是我正在研究的一个版本：http://medschoolgunners.com/sandbox/3d/。

我试图让灰色圆锥与未标记的红色矢量完全对齐。 IE。我希望圆锥的尖端与向量完全对齐，并从原点指向该方向。

这是我现在拥有的代码：

    //FUNCTION TO CREATE A CYLINDER
function create_cylinder(radiusTop,radiusBottom, height, segmentsRadius, segmentsHeight, openEnded, color)
{
var material = new THREE.MeshLambertMaterial({
    color: color, //0x0000ff
    opacity: 0.2
});
var cylinder = new THREE.Mesh(new THREE.CylinderGeometry(radiusTop,radiusBottom, height, segmentsRadius, segmentsHeight, openEnded), material);

cylinder.overdraw = true;

return cylinder;
}

//ALIGN THE CYLINDER TO A GIVEN VECTOR
var alignVector=new THREE.Vector3(-50,50,50); //the vector to be aligned with

var newcylinder = create_cylinder(0.1, 10, 40, 50, 50, false, "0x0ff0f0");  // the object to be aligned with the vector above

var cylinderQuaternion = new THREE.Quaternion();
cylinderQuaternion.setFromEuler(alignVector);
newcylinder.useQuaternion = true;
newcylinder.quaternion=cylinderQuaternion;

scatterPlot.add(newcylinder);

Answer 1

如果你有一个任意向量：

var vector = new THREE.Vector3(100, 60, 20);

您可以将对象（例如圆柱体）与矢量对齐，如下所示：

var geometry = new THREE.CylinderGeometry(2, 2, vector.length(), 4, 4);
var mesh = new THREE.Mesh(geometry, someMaterial);
var axis = new THREE.Vector3(0, 1, 0);
mesh.quaternion.setFromUnitVectors(axis, vector.clone().normalize());

其中axis 是圆柱体的原始方向（向上）。

您也可以像这样移动圆柱体以匹配矢量的位置：

mesh.position.copy(vector.clone().multiplyScalar(0.5));

这会将圆柱体的一端放在0, 0, 0，另一端放在100, 60, 20，因为我将圆柱体长度设置为vector.length()。

Answer 2

我知道这是一个老问题，但如果有人仍然想知道，对我有用的是将矢量添加到网格位置并使用 lookAt 将其与矢量对齐：

//Mesh to align
var material = new THREE.MeshLambertMaterial({color: 0x0000ff});
var cylinder = new THREE.Mesh(new THREE.CylinderGeometry(10, 10, 15), material);

//vector to align to
var vector = new THREE.Vector3(
    5,//x
    10,//y
    15 //z
);

//create a point to lookAt
var focalPoint = new THREE.Vector3(
    cylinder.position.x + vector.x,
    cylinder.position.y + vector.y,
    cylinder.position.z + vector.z
);

//all that remains is setting the up vector (if needed) and use lookAt
cylinder.up = new THREE.Vector3(0,0,1);//Z axis up
cylinder.lookAt(focalPoint); 

Answer 3

很遗憾，我没有使用过四元数，所以帮不上什么忙。在我看来，需要进行一些偏移，因为圆柱体的枢轴位于网格的中心，而不是一端。

如果稍微玩一下矩阵，我会得到不错的结果。

这是一种方法，使用 Mesh 的 lookAt() 方法：

var HALF_PI = -Math.PI * .5;
var p1 = new THREE.Vector3(Math.random()-.5,Math.random()-.5,Math.random()-.5).multiplyScalar(30);
var p2 = new THREE.Vector3(Math.random(),Math.random(),Math.random()).multiplyScalar(300);
var halfLength = diff.length() * .5;

var c = new THREE.CylinderGeometry(10, 10, halfLength * 2, 12, 1, false );
var orientation = new THREE.Matrix4();
orientation.setRotationFromEuler(new THREE.Vector3(HALF_PI,0,0));//rotate on X 90 degrees
orientation.setPosition(new THREE.Vector3(0,0,halfLength));//move half way on Z, since default pivot is at centre
c.applyMatrix(orientation);//apply transformation for geometry

var m = new THREE.Mesh( c, new THREE.MeshLambertMaterial( { color: 0x009900, wireframe: true, shading: THREE.FlatShading } ) );
scene.add(m);
m.lookAt(p2);//tell mesh to orient itself towards p2
//just for debugging - to illustrate orientation
m.add(new THREE.Axes());

//visualize p1,p2 vectors
var PI2 = Math.PI * 2;
var program = function ( context ) {

    context.beginPath();
    context.arc( 0, 0, 1, 0, PI2, true );
    context.closePath();
    context.fill();

}

particleMaterial = new THREE.ParticleCanvasMaterial( { color: 0x990000, program: program } );
var pp1 = new THREE.Particle( new THREE.ParticleCanvasMaterial( { color: 0x990000, program: program } ) );
pp1.scale.multiplyScalar(10);
pp1.position.copy(p1);
scene.add( pp1 );   
var pp2 = new THREE.Particle( new THREE.ParticleCanvasMaterial( { color: 0x009900, program: program } ) );
pp2.scale.multiplyScalar(10);
pp2.position.copy(p2);
scene.add( pp2 );

这应该绘制一个从 p1 开始，在 p2 结束并朝向它的圆柱体。 偏移可能需要一些调整，但几何图形非常接近矢量方向。

还有更长版本的手动计算矩阵，而不是依赖于lookAt() 功能：

plane.add(getCylinderBetweenPoints(p1,p2,new THREE.MeshLambertMaterial( { color: 0x009900, wireframe: true, shading: THREE.FlatShading } )));

function getCylinderBetweenPoints(point1,point2,material){
    var HALF_PI = -Math.PI * .5;
    var diff = new THREE.Vector3().sub(point1,point2);//delta vector
    var halfLength = diff.length() * .5;
    var c = new THREE.CylinderGeometry(10, 10, halfLength * 2, 12, 1, false );
    var orientation = new THREE.Matrix4();//a new orientation matrix to offset pivot
    var offsetRotation = new THREE.Matrix4();//a matrix to fix pivot rotation
    var offsetPosition = new THREE.Matrix4();//a matrix to fix pivot position
    orientation.lookAt(point1,point2,new THREE.Vector3(0,1,0));//look at destination
    offsetRotation.setRotationX(HALF_PI);//rotate 90 degs on X
    offsetPosition.setPosition(new THREE.Vector3(-point1.x,diff.length()*.5+point1.z,point1.y*.5));//move by pivot offset on Y
    orientation.multiplySelf(offsetRotation);//combine orientation with rotation transformations
    orientation.multiplySelf(offsetPosition);//combine orientation with position transformations
    c.applyMatrix(orientation);//apply the final matrix
    var m = new THREE.Mesh( c, material );
    m.add(new THREE.Axes());
    return m;
}

var PI2 = Math.PI * 2;
var program = function ( context ) {

    context.beginPath();
    context.arc( 0, 0, 1, 0, PI2, true );
    context.closePath();
    context.fill();

}

//visualize p1,p2 vectors
particleMaterial = new THREE.ParticleCanvasMaterial( { color: 0x990000, program: program } );
var pp1 = new THREE.Particle( new THREE.ParticleCanvasMaterial( { color: 0x990000, program: program } ) );
pp1.scale.multiplyScalar(10);
pp1.position.copy(p1);
plane.add( pp1 );   
var pp2 = new THREE.Particle( new THREE.ParticleCanvasMaterial( { color: 0x009900, program: program } ) );
pp2.scale.multiplyScalar(10);
pp2.position.copy(p2);
plane.add( pp2 );

从我在您的代码中看到的情况来看，这看起来比使用四元数更多。如果 setFromEuler 对方向有魔力，那么网格的几何图形仍然可能需要移动（从一端而不是中心旋转）

HTH