Terrain Camera

The TerrainCamera behaves almost exactly like FirstPersonCamera. The only difference is that whenever the from position changes, we raise or lower the camera so it floats at some fixed offset above the terrain surface.

Because the two cameras are so similar, we might be tempted to have TerrainCamera inherit from FirstPersonCamera. That's a nice idea, but there's a problem. The FirstPersonCamera constructor calls reorient, which considers the camera's position. A TerrainCamera should therefore adjust the camera's y-position before reorient gets called. But a subclass can't do anything before its superclass's constructor has been called.

When inheritance doesn't work, we have other options. The most expedient option is to copy and paste the FirstPersonCamera class, name the clone TerrainCamera, and make the following edits to the class:

class TerrainCamera {
  // ...
  field: Field2;
  offset: number;
  factors: Vector3;

  constructor(from: Vector3, to: Vector3, field: Field2, offset: number, factors: Vector3) {
    // ...
    this.worldUp = new Vector3(0, 1, 0);
    this.field = field;
    this.offset = offset;
    this.factors = factors;
    this.adjustY();
    this.reorient();
  }

  // ...

  advance(distance: number) {
    // ...
    this.adjustY();
    this.reorient();
  }

  strafe(distance: number) {
    // ...
    this.adjustY();
    this.reorient();
  }
}

class TerrainCamera {
  // ...
  field: Field2;
  offset: number;
  factors: Vector3;

  constructor(from: Vector3, to: Vector3, field: Field2, offset: number, factors: Vector3) {
    // ...
    this.worldUp = new Vector3(0, 1, 0);
    this.field = field;
    this.offset = offset;
    this.factors = factors;
    this.adjustY();
    this.reorient();
  }

  // ...

  advance(distance: number) {
    // ...
    this.adjustY();
    this.reorient();
  }

  strafe(distance: number) {
    // ...
    this.adjustY();
    this.reorient();
  }
}

Whenever from changes—as it does in the constructor, advance, and strafe—we immediately call adjustY, which we haven't written yet. We implement it by unscaling the camera's xz-position, looking up the height, and raising or lower the camera so it floats above the terrain.

Let's test this. Move around in this renderer, which uses the code above:

The movement is very choppy. Why? Because we're only using the known heights at the vertices, while the camera is skating between the vertices. We need a way to guess the heights at arbitrary locations on the terrain grid. That sounds like a job for lerp.

There's a catch. Our lerp function only handles interpolation along one dimension and between two known data points. A terrain is indexed in two dimensions. How do we extend linear interpolation to a higher-dimensional space? Step through this breakdown of the algorithm to see how it's done:

Here lies a point that doesn't land neatly on the terrain. This point doesn't have a defined height, so we are going to make one up.

We aren't going to make up a random height, however. The four neighbors around the point will guide our decision.

We need to know the integer coordinates of the four neighboring vertices.

This point's coordinates will be between the integer coordinates of the neighbors. Here the point is at [18.7, 33.2]. The floor and ceiling of these coordinates give us the neighbors' coordinates.

We also need to know what the heights are at the four neighboring vertices. These are given by the Field2.get method.

Now we are ready to start calculating the in-between point's value. Blending all four neighbors together at once is too confusing. Instead we think about this bottom point, which is between just two neighbors.

That bottom point's fractional x-component is 0.7. That's means it's 70% of the way along the southern edge of the cell. Our lerp function tells us its value: $$ \begin{array}{c} 75 + 0.7 \times (97 - 75) \\ \downarrow \\ 90.4 \end{array} $$

Next we turn our attention to the top point, which is between the other two neighbors.

The top point's fractional x-component is also 0.7. Our lerp function tells us its value: $$ \begin{array}{c} 94 + 0.7 \times (62 - 94) \\ \downarrow \\ 71.6 \end{array} $$

Look at that. Now the point in the middle lies on a line between two known values.

The middle point's fractional z-component is 0.2. Our lerp function tells us its value: $$ \begin{array}{c} 90.4 + 0.2 \times (71.6 - 90.4) \\ \downarrow \\ 86.64 \end{array} $$ Three lerps later, we have the point's interpolated height.

previous next

Linearly interpolating between four points in two dimensions is called bilinear interpolation or blerp. Bilinear interpolation reduces down to three linear interpolations, two along one of the dimensions and a third along the other dimension.

We'll eventually need blerping for more than just terrain, so let's add a reusable blerp method to the Field2 class.

The adjustY must itself be adjusted. As before, it unscales the camera's xz-coordinates, looks up the height, and sets the camera's y-position. But this time it doesn't truncate the xz-coordinates to integers. Instead it queries the intermediate height using the blerp method.

See the effect of this interpolation by enabling the use of blerp in the renderer above.

Summary

WebGL has no notion of a viewer. It just renders whatever's in the unit box. To render a different chunk of the world, we compose translation and rotation matrices that transform the chunk into the unit box. This task is complex enough to warrant camera abstractions. These include several behaviors that change the camera interactively: advance, strafe, yaw, and pitch the viewer. A first-person camera makes the viewer feel like a character in the scene. A third-person camera puts the viewer over the shoulder of an avatar. These cameras fly through a scene without constraint. To offer a more grounded interaction, we load in a heightmap of elevation data and expand it into a trimesh. A terrain camera stays pinned to the terrain as the viewer moves about. Heights are bilinearly interpolated from the heightmap.