Off-axis frustum

since 0.7.0 Views, picking and input

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An ordinary perspective camera has its axis down the middle: the same angle opens to the left as to the right. A headset lens is not built that way, and neither is a window in a wall that a player looks through from one side. OffAxisProjection describes a frustum whose four sides are given separately, so the axis can sit anywhere inside it.

Step 1: Start from a symmetric one #

The easiest way to build an off-axis frustum is to start from a symmetric one and then move its sides. OffAxisProjection.symmetric builds the frustum an ordinary perspective camera of the same field of view would have.

final OffAxisProjection symmetric = OffAxisProjection.symmetric(
  fovYRadians: 0.9,
  aspect: 16 / 9,
);

Step 2: Shift it #

Sliding tanLeft and tanRight by the same amount keeps the frustum's width the same but moves its axis. This is the shape a stereo eye or a portal needs: the lens is not centred on what it is looking at.

_off = symmetric.copyWith(
  tanLeft: symmetric.tanLeft - shift,
  tanRight: symmetric.tanRight - shift,
);

Note. The four values are tangents of angles from the view axis, not angles themselves. That is what the matrix needs directly, and it is what a headset runtime already hands over as XrFovf.

Step 3: Watch the sphere move #

Drag the slider and the sphere slides across the frame without the camera itself turning. A symmetric camera cannot do this: turning it would rotate the whole world with it. An off-axis one reframes without rotating, which is the one thing this projection is for.

_off = symmetric.copyWith(
  tanLeft: symmetric.tanLeft - shift,
  tanRight: symmetric.tanRight - shift,
);