Rotating Camera around a Vector3 Point in Three.js

Question

Rotating Camera around a Vector3 Point in Three.js

Let me get straight to the point - math is not my strong suit. What may be a piece of cake for you is like solving complex equations in outer space for me.

Currently, I am using Three.js with CSS3DRenderer to construct a virtual art gallery.

What I really need is a first-person perspective, similar to that of a FPS game.

I've managed to make the camera move forward, backward, left, and right successfully.

However, when it comes to rotating the camera, let's just say the results are not what I expected.

The issue lies in my camera rotating on its local axis instead of the viewport itself.

What I truly desire is for the camera to orbit around a specific pivot point/vector, and then readjust its focus using Object3d.lookAt().

I understand that I could simply parent the camera as a child of another object and manipulate the object's axis to achieve this effect. But personally, I prefer to delve into the mathematical calculations myself.

In essence, I want to comprehend how to have one vector point rotate around another, and the mathematical representation behind it.

I am not looking to take the easy route by relying on pre-made scripts like the three.js pointer_lock controls. I am eager to roll up my sleeves and tackle the challenge head-on with pure mathematics.

Any guidance or references to tutorials would be greatly valued and appreciated!

javascript three.js trigonometry vector-space

Answer 1

Answer №1

Check out this demonstration of a camera rotating around a box.

The key to making this work is understanding that applying a rotation matrix always rotates an object around the origin. This differs from simply adjusting the rotation property, which rotates the object around its own center. By positioning the camera 200 units away from the origin and then applying the rotation matrix, the camera will rotate in a circular motion around the origin, effectively rotating around the box at the origin. The lookAt function is then used to direct the camera towards the box.

If you're interested in delving deeper into this topic, here's a resource providing a more detailed explanation:

var canvas = document.getElementById('canvas');
var scene = new THREE.Scene();
var renderer = new THREE.WebGLRenderer({canvas: canvas, antialias: true});
var camera = new THREE.PerspectiveCamera(45, canvas.clientWidth / canvas.clientWidth, 1, 1000);

var geometry = new THREE.BoxGeometry(50, 50, 50);
var material = new THREE.MeshBasicMaterial({color: '#f00'});
var box = new THREE.Mesh(geometry, material);
scene.add(box);

// Ensure camera moves forward to prevent spinning in place.
camera.position.z = 200;

var period = 5; // time taken for one full rotation (in seconds)
var clock = new THREE.Clock();
var matrix = new THREE.Matrix4(); // Allocate empty matrix for performance optimization.
render();

function render() {
  requestAnimationFrame(render);
  if (canvas.width !== canvas.clientWidth || canvas.height !== canvas.clientHeight) {
    // Auto-resize mechanism.
    renderer.setSize(canvas.clientWidth, canvas.clientHeight, false);
    camera.aspect = canvas.clientWidth /  canvas.clientHeight;
    camera.updateProjectionMatrix();
  }

  // Create a rotation matrix that rotates every 'period' seconds.
  matrix.makeRotationY(clock.getDelta() * 2 * Math.PI / period);

  // Apply the matrix to rotate the camera.
  camera.position.applyMatrix4(matrix);

  // Make camera look at the box.
  camera.lookAt(box.position);

  // Render the scene.
  renderer.render(scene, camera);
}

html, body, #canvas {
  margin: 0;
  padding: 0;
  width: 100%;
  height: 100%;
}

<script src="https://cdnjs.cloudflare.com/ajax/libs/three.js/r77/three.js"></script>
<canvas id="canvas"></canvas>

Answer 2

Check out this demonstration of a camera rotating around a box.

The key to making this work is understanding that applying a rotation matrix always rotates an object around the origin. This differs from simply adjusting the rotation property, which rotates the object around its own center. By positioning the camera 200 units away from the origin and then applying the rotation matrix, the camera will rotate in a circular motion around the origin, effectively rotating around the box at the origin. The lookAt function is then used to direct the camera towards the box.

If you're interested in delving deeper into this topic, here's a resource providing a more detailed explanation:

var canvas = document.getElementById('canvas');
var scene = new THREE.Scene();
var renderer = new THREE.WebGLRenderer({canvas: canvas, antialias: true});
var camera = new THREE.PerspectiveCamera(45, canvas.clientWidth / canvas.clientWidth, 1, 1000);

var geometry = new THREE.BoxGeometry(50, 50, 50);
var material = new THREE.MeshBasicMaterial({color: '#f00'});
var box = new THREE.Mesh(geometry, material);
scene.add(box);

// Ensure camera moves forward to prevent spinning in place.
camera.position.z = 200;

var period = 5; // time taken for one full rotation (in seconds)
var clock = new THREE.Clock();
var matrix = new THREE.Matrix4(); // Allocate empty matrix for performance optimization.
render();

function render() {
  requestAnimationFrame(render);
  if (canvas.width !== canvas.clientWidth || canvas.height !== canvas.clientHeight) {
    // Auto-resize mechanism.
    renderer.setSize(canvas.clientWidth, canvas.clientHeight, false);
    camera.aspect = canvas.clientWidth /  canvas.clientHeight;
    camera.updateProjectionMatrix();
  }

  // Create a rotation matrix that rotates every 'period' seconds.
  matrix.makeRotationY(clock.getDelta() * 2 * Math.PI / period);

  // Apply the matrix to rotate the camera.
  camera.position.applyMatrix4(matrix);

  // Make camera look at the box.
  camera.lookAt(box.position);

  // Render the scene.
  renderer.render(scene, camera);
}

html, body, #canvas {
  margin: 0;
  padding: 0;
  width: 100%;
  height: 100%;
}

<script src="https://cdnjs.cloudflare.com/ajax/libs/three.js/r77/three.js"></script>
<canvas id="canvas"></canvas>

Answer 3

Answer №2

To efficiently handle positioning and movement of a camera in relation to an object, it is common practice to establish a variable called camera_pivot using the object3D() method at the same coordinates as the object itself. By making the camera a child of this pivot, adjusting its position to create the desired viewing distance, and rotating the object, smooth observations can be achieved.

The flexibility provided by object3D() allows for easy adjustments to both the object's movement and rotation according to specific requirements. This approach not only simplifies coding but also enhances performance.

Utilizing methods like camera_pivot.translateX(), camera_pivot.rotateX(), and camera_pivot.lookAt(obj) on object3D provides further control over the camera's behavior.

In contrast, attempting to manipulate camera and object interactions without utilizing object3D can lead to complications and unintended consequences within the scene.

Answer 4

To efficiently handle positioning and movement of a camera in relation to an object, it is common practice to establish a variable called camera_pivot using the object3D() method at the same coordinates as the object itself. By making the camera a child of this pivot, adjusting its position to create the desired viewing distance, and rotating the object, smooth observations can be achieved.

The flexibility provided by object3D() allows for easy adjustments to both the object's movement and rotation according to specific requirements. This approach not only simplifies coding but also enhances performance.

Utilizing methods like camera_pivot.translateX(), camera_pivot.rotateX(), and camera_pivot.lookAt(obj) on object3D provides further control over the camera's behavior.

In contrast, attempting to manipulate camera and object interactions without utilizing object3D can lead to complications and unintended consequences within the scene.

Rotating Camera around a Vector3 Point in Three.js

Answer №1

Answer №2

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