 | Introduction |  |
In 3D graphics, the camera is a virtual viewpoint through which we see the scene. Like a physical camera, a virtual camera determines what part of a scene is visible and how it’s displayed. This chapter explores how to set up, manipulate, and animate a camera in WebGPU, discussing concepts like camera positioning, movement, and the math behind transformations. We’ll also examine how to animate a camera along a path to create smooth scene transitions and dynamic viewpoints.
Camera Motion vs. Scene Motion
It’s essential to differentiate between moving the camera and moving objects in the scene. Moving the camera alters the viewpoint from which we observe the scene, while moving an object changes its position within the scene. When the camera moves, the entire scene appears to shift in the opposite direction, as though the viewer's perspective itself is moving.
A Camera Definition
In WebGPU, a camera is defined by its position in space, the direction it points, and the up vector, which determines the camera's orientation. The `lookAt` function in `glMatrix` is often used to set up a camera in WebGPU. This function creates a view matrix that orients the camera correctly based on these parameters.
Specifying a Virtual Camera
To set up a virtual camera, we define three key properties:
• Position: The camera’s location in 3D space.
• Target: The point in space the camera is looking at.
• Up Vector: Specifies the camera's vertical direction, typically `[0, 1, 0]` for a camera with a standard upright orientation.
Example code to specify a camera with lookAt :
import { mat4, vec3 } from 'gl-matrix';
let viewMatrix = mat4.create();
let cameraPosition = vec3.fromValues(0, 5, 10);
let target = vec3.fromValues(0, 0, 0);
let up = vec3.fromValues(0, 1, 0);
mat4.lookAt(viewMatrix, cameraPosition, target, up);
| Camera Math | |
Understanding the math behind a camera's transformations allows us to set up complex camera movements.
A Camera Definition
The camera’s view matrix is the product of transformations that place it at a default location, rotate it to face the target, and orient it correctly based on the up vector.
Moving a Camera to its Default Location and Orientation
A camera starts at an origin point, typically `[0, 0, 0]`, facing a default direction (e.g., negative z-axis). Moving the camera to a different position and orientation requires a combination of translation and rotation.
To rotate a camera to face its target, we calculate the vector between the camera position and the target. We use the cross product to align the up vector with the camera’s orientation. This results in a rotation that reorients the camera.
`lookAt` Implementation
The `lookAt` function automates setting up the camera by calculating the necessary transformations to face a specified target. This function combines translation and rotation transformations into a single view matrix.
| Camera Movement (Common Camera Movements) | |
Cameras often move in three main ways:
1. Panning: Moving horizontally across the scene.
2. Tilting: Rotating the camera up or down.
3. Trucking: Moving forward or backward along the camera's viewing direction.
Camera Motions using `lookAt`
Using `lookAt`, we can dynamically update the camera's position and target to simulate these movements, resulting in smooth camera transitions and animations.
| Moving a Camera | |
Camera motion includes both linear movements and rotations. Moving the camera involves changing its position, while rotations adjust its orientation.
Truck Motion
Trucking refers to moving the camera forward or backward along its view direction. This effect is achieved by translating the camera position along the viewing vector.
Example code for trucking:
let direction = vec3.create();
vec3.subtract(direction, target, cameraPosition);
vec3.normalize(direction, direction);
vec3.scale(direction, direction, truckDistance); // truckDistance can be positive or negative
vec3.add(cameraPosition, cameraPosition, direction);
mat4.lookAt(viewMatrix, cameraPosition, target, up);
Using `lookAt` Parameters
To move the camera smoothly, update the `lookAt` parameters frame-by-frame, adjusting position and target values based on the desired direction and speed.
Modify a Camera’s Definition
Updating a camera’s position and target dynamically alters its definition, allowing flexible control over its viewpoint.
| Rotating a Camera (Tilt Motion) | |
Tilting involves rotating the camera up or down along its x-axis, changing the view angle while keeping the camera’s position fixed.
Using `lookAt` to Tilt
Adjusting the target point to a higher or lower position, we can create a tilt effect using lookAt .
Example code for tilting:
target[1] += tiltAmount; // Adjust the y-coordinate of the target for tilting
mat4.lookAt(viewMatrix, cameraPosition, target, up);
Modify a Camera’s Definition
Directly modifying the camera’s target point enables precise control over tilt and other rotation effects.
| Points Along a Path | |
Moving the camera along a path creates smooth transitions and is common in animations and fly-throughs.
Parametric Equations
Parametric equations allow us to define a path by varying a parameter \( t \). For instance, a simple linear path from point A to point B is defined by the equation:
\[
P(t) = (1 - t)A + tB
\]
where \( t \) varies from 0 to 1.
Basis Functions
Basis functions can create more complex paths, including curves and splines, by defining intermediate points.
Circular Paths
To move the camera along a circular path, parametric equations in terms of sine and cosine functions provide the x and z coordinates for circular motion, with the y-coordinate remaining constant.
Example code for circular path:
const radius = 10;
const angle = time * speed; // time and speed control rotation speed
cameraPosition[0] = Math.cos(angle) * radius;
cameraPosition[2] = Math.sin(angle) * radius;
mat4.lookAt(viewMatrix, cameraPosition, target, up);
| Timing Along a Path | |
Adjusting the camera’s speed and acceleration along a path can create smooth, realistic motion.
Speed and Acceleration
Applying constant or variable speed affects the rate at which the camera progresses along its path.
Ignore Acceleration
Without acceleration, the camera maintains a constant speed, simplifying calculations.
Include Acceleration
Incorporating acceleration involves adding a changing factor to the camera’s speed, providing more dynamic motion.
| Screen Updates and Animation | |
Double buffering helps prevent flickering by rendering the scene to an off-screen buffer before displaying it, ensuring smoother frame transitions.
Updating the Screen
Continuously updating the camera’s parameters and redrawing the scene achieves fluid animation.
The `requestAnimationFrame` Function
In JavaScript, `requestAnimationFrame` synchronizes updates with the display’s refresh rate, enabling smooth animations.
Example code using `requestAnimationFrame`:
function animate() {
// Update camera position or target here
mat4.lookAt(viewMatrix, cameraPosition, target, up);
// Render scene here
requestAnimationFrame(animate);
}
animate();
| Summary | |
This chapter covered camera setup, movement, and animation in WebGPU. Using transformations like `lookAt`, we can position and orient a virtual camera, while path-based animations provide smooth motion for dynamic scenes. Understanding camera math, common movements, and rendering techniques like double buffering is essential for creating immersive 3D experiences.
|
