Camera, focus, and 3D

Matemium combines a document-like tape camera with a free 3D world. The camera should clarify relationships, not become decoration.

Focus an existing element

plot_id = tape.add_math(r"y = x^2")

builder.add_camera_focus(
    plot_id,
    mode="isolate",
    zoom=2.0,
    hold_time=1.2,
)

The viewport-fit system caps isolate zoom when necessary so the target remains inside the frame.

Focus modes:

isolate — move attention to the target itself.
overlay — present a magnified overlay while retaining wider context.

Explicit tape movement

builder.add_camera_move(dy=3.5)

Prefer automatic reveal and focus when they already express the intended motion. Use explicit camera movement when the transition itself carries meaning.

Add a mathematical surface

builder.add_3d(
    r"z = \sin(x)\cos(y)",
    pitch=50,
    style={
        "width": 5.2,
        "align": "center",
        "margin-bottom": 0.5,
    },
)

Flat content remains in sheet view. A 3D moment may tilt the camera, then return to tape content.

Add and inspect a solid

Project helpers can build a subject-specific arrangement from generic solids:

solid_id = add_inscribed_pair(
    builder,
    id="inscribed_pair",
    cube_side=2.4,
)

builder.add_solid_lift(solid_id, lift=1.8, run_time=1.3)
builder.add_camera_inspect(
    solid_id,
    path=inscribed_tangency_study_path(builder),
    curve="linear",
    return_to_sheet=True,
)

add_solid_lift raises a solid above a tape for inspection. It is not a general tape-switching mechanism.

World coordinates

Matemium’s world uses:

Axis	Meaning
X	Horizontal placement
Y	Tape scroll direction
Z	Depth above or below a tape

A tape may itself be transformed in the larger world. Its content layout remains local to that tape.

Camera guidelines

Establish the object before moving close.
Hold long enough for viewers to inspect what the movement reveals.
Avoid orbiting without an explanatory purpose.
Preserve labels or add camera-facing labels for 3D objects.
Return to the reasoning context after an inspection.
Validate camera behavior in the final target orientation.