bencher.results.manim_cartesian.cartesian_product_scene

Dimensional extrusion animation using PIL.

Shows how each dimension builds on the last:: point –dim1–> line –dim2–> grid –dim3–> stack –repeat–> extrude –over_time–> film strip –dim4+–> sets of sets …

Renders frames directly with PIL (fast), saves as animated PNG (APNG).

Classes

`Shape`	Recursive shape representation for dimensional extrusion.
`TimelineShape`	Film-strip timeline for the over_time dimension.
`StrobeShape`	Shape with a glowing border and tally-mark counter.

Functions

`render_shape_to_image`(→ PIL.Image.Image)	Render shape into an offscreen image scaled to fit target_w x target_h.
`_generate_unique_filename`(→ str)	Generate a unique filename based on animation parameters.
`_get_font`(size)	Get a font, falling back to default if no TTF available.
`_direction_for`(→ str)	Map dimension index to layout direction.
`render_animation`(→ str)	Render the dimensional extrusion animation.

Module Contents

bencher.results.manim_cartesian.cartesian_product_scene.logger

bencher.results.manim_cartesian.cartesian_product_scene.CELL_SIZE = 20

bencher.results.manim_cartesian.cartesian_product_scene.CELL_GAP = 3

bencher.results.manim_cartesian.cartesian_product_scene.DIM_PALETTE = [(150, 190, 240), (240, 160, 155), (150, 220, 160), (245, 225, 140), (220, 170, 235), (245, 200,...

bencher.results.manim_cartesian.cartesian_product_scene.CELL_BORDER = (180, 180, 180)

bencher.results.manim_cartesian.cartesian_product_scene.BG_COLOR = (255, 255, 255)

bencher.results.manim_cartesian.cartesian_product_scene.LABEL_COLOR = (30, 30, 30)

bencher.results.manim_cartesian.cartesian_product_scene.DEPTH_DX = 10

bencher.results.manim_cartesian.cartesian_product_scene.DEPTH_DY = -8

bencher.results.manim_cartesian.cartesian_product_scene.GROUP_GAP = 20

bencher.results.manim_cartesian.cartesian_product_scene.GAP = '...'

bencher.results.manim_cartesian.cartesian_product_scene.render_shape_to_image(shape: Shape, target_w: int, target_h: int, bg_color: tuple[int, int, int] = BG_COLOR, alpha: float = 1.0) → PIL.Image.Image

Render shape into an offscreen image scaled to fit target_w x target_h.

The returned image is at most target_w x target_h and centered content-wise.

bencher.results.manim_cartesian.cartesian_product_scene._generate_unique_filename(cfg: bencher.results.manim_cartesian.cartesian_product_cfg.CartesianProductCfg, width: int, height: int) → str: Generate a unique filename based on animation parameters.

bencher.results.manim_cartesian.cartesian_product_scene._get_font(size: int): Get a font, falling back to default if no TTF available.

class bencher.results.manim_cartesian.cartesian_product_scene.Shape(children: list[Shape] | None = None, direction: str = 'right', depth: int = 0, color_index: int = 0)

Recursive shape representation for dimensional extrusion.

A Shape is either a leaf (single cell) or a collection of sub-shapes arranged along an axis. depth tracks nesting level so that higher-dimensional extrusions use wider gaps.

children = None

direction = 'right'

depth = 0

color_index = 0

_cached_size = None

property is_leaf: bool

property gap: int

Gap between children.

Depth 0-2 (first two spatial dims forming the basic grid): tight CELL_GAP. Depth 3 (stack direction): uses isometric offset, gap not used. Depth 4+ (sets of stacks, sets of sets): GROUP_GAP scaling with depth.

size() → tuple[int, int]: Return (width, height) in pixels. Cached — tree structure is immutable.

draw(img: PIL.ImageDraw.ImageDraw, x: int, y: int, alpha: float = 1.0): Draw this shape at position (x, y) on the image.

extrude(n: int, direction: str, color_index: int | None = None) → Shape: Create a new shape by extruding this one n times along direction.

_deep_copy() → Shape

_deep_copy_recolored(color_index: int) → Shape: Copy and recolor in a single traversal.

bencher.results.manim_cartesian.cartesian_product_scene._direction_for(dim_index: int) → str: Map dimension index to layout direction.

bencher.results.manim_cartesian.cartesian_product_scene.FILM_COLOR = (35, 35, 38)

bencher.results.manim_cartesian.cartesian_product_scene.FILM_EDGE = (25, 25, 28)

bencher.results.manim_cartesian.cartesian_product_scene.FILM_FRAME_BORDER = (90, 90, 95)

bencher.results.manim_cartesian.cartesian_product_scene.FILM_LABEL_COLOR = (100, 100, 100)

bencher.results.manim_cartesian.cartesian_product_scene.FILM_PAD = 6

bencher.results.manim_cartesian.cartesian_product_scene.FILM_FRAME_PAD = 10

bencher.results.manim_cartesian.cartesian_product_scene.FILM_FRAME_GAP = 16

bencher.results.manim_cartesian.cartesian_product_scene.FILM_SPROCKET_W = 8

bencher.results.manim_cartesian.cartesian_product_scene.FILM_SPROCKET_H = 14

bencher.results.manim_cartesian.cartesian_product_scene.FILM_SPROCKET_R = 2

bencher.results.manim_cartesian.cartesian_product_scene.FILM_SPROCKET_SPACING = 14

bencher.results.manim_cartesian.cartesian_product_scene.FILM_SPROCKET_MARGIN = 4

bencher.results.manim_cartesian.cartesian_product_scene.FILM_LABEL_H = 18

class bencher.results.manim_cartesian.cartesian_product_scene.TimelineShape(inner: Shape, count: int)

Bases: Shape

Film-strip timeline for the over_time dimension.

Each time step is a “frame” in a horizontal film strip with sprocket holes along top and bottom edges — unmistakably film.

The film chrome (sprockets, borders, padding) is always rendered at a fixed pixel size. The inner shape is scaled to fit within a constant frame window so the strip looks the same regardless of content complexity.

FRAME_W = 100

FRAME_H = 80

inner

count

_skip_labels = False

property is_leaf: bool

_outer_frame_size() → tuple[int, int]: Size of each frame including padding.

size() → tuple[int, int]: Return (width, height) in pixels. Cached — tree structure is immutable.

draw(img: PIL.ImageDraw.ImageDraw, x: int, y: int, alpha: float = 1.0): Draw this shape at position (x, y) on the image.

static _draw_sprockets(img: PIL.ImageDraw.ImageDraw, strip_x: int, row_y: int, strip_w: int): Draw a row of rounded sprocket holes across the strip width.

strip_size() → tuple[int, int]: Size of the film strip excluding the label row below.

draw_without_labels(img: PIL.ImageDraw.ImageDraw, x: int, y: int) → None: Draw the film strip without frame labels, preserving previous state.

render_strip_image(v_scale: float = 1.0) → PIL.Image.Image

Render the strip (without labels) into an offscreen image.

The strip is drawn at full resolution and then uniformly scaled by v_scale (typically chosen to fit the canvas height). The returned image can be pasted directly — PIL clips any overflow naturally.

draw_label_overlay_for_viewport(img: PIL.ImageDraw.ImageDraw, strip_x: int, strip_y: int, strip_h: int, scale: float, canvas_w: int) → None: Draw frame labels at fixed pixel size for frames visible on canvas.

_deep_copy() → Shape

class bencher.results.manim_cartesian.cartesian_product_scene.StrobeShape(inner: Shape, count: int, cfg: bencher.results.manim_cartesian.cartesian_product_cfg.CartesianProductCfg, flash: float = 0.0)

Bases: Shape

Shape with a glowing border and tally-mark counter.

flash (0–1) controls the glow intensity for animation frames. All visual tunables are read from cfg (a CartesianProductCfg).

inner

count

cfg

flash = 0.0

_skip_tally = False

property is_leaf: bool

size() → tuple[int, int]: Return (width, height) in pixels. Cached — tree structure is immutable.

draw(img: PIL.ImageDraw.ImageDraw, x: int, y: int, alpha: float = 1.0): Draw this shape at position (x, y) on the image.

_draw_tally(img, mx0, my, avail_w, color, c)

Proper tally marks (vertical lines, diagonal strike every 5) + xN label.

Tallies grow from the left. The xN number is always on the right. Only draws as many complete groups/marks as fit cleanly; the label alone conveys the count when space is tight.

content_box_size() → tuple[int, int]: Size of border + inner shape, excluding the tally mark row.

draw_without_tally(img: PIL.ImageDraw.ImageDraw, x: int, y: int) → None: Draw the shape without tallies, preserving previous state.

draw_tally_overlay(img: PIL.ImageDraw.ImageDraw, anchor_x: int, anchor_y: int, avail_w: int): Draw tally marks at fixed pixel size on the final frame.

draw_tally_overlay_for_box(img: PIL.ImageDraw.ImageDraw, box_x: int, box_y: int, box_w: int, box_h: int) → None

Draw fixed-size tally overlay below a rendered box.

Spacing is derived from cfg fields so layout stays consistent when configuration changes.

_deep_copy() → Shape

bencher.results.manim_cartesian.cartesian_product_scene.render_animation(cfg: bencher.results.manim_cartesian.cartesian_product_cfg.CartesianProductCfg, width: int = 400, height: int = 300, fps: int = 15, step_frames: int = 4, output_dir: str = 'cachedir/cartesian') → str

Render the dimensional extrusion animation.

Parameters:

cfg (CartesianProductCfg) – Sweep configuration.
width (int) – Video resolution.
height (int) – Video resolution.
fps (int) – Frames per second.
step_frames (int) – Frames to show each extrusion step (per sub-copy).
output_dir (str) – Directory for the output video.

Returns:

Path to the output animation file.

Return type:

str

`logger`
`CELL_SIZE`
`CELL_GAP`
`DIM_PALETTE`
`CELL_BORDER`
`BG_COLOR`
`LABEL_COLOR`
`DEPTH_DX`
`DEPTH_DY`
`GROUP_GAP`
`GAP`
`FILM_COLOR`
`FILM_EDGE`
`FILM_FRAME_BORDER`
`FILM_LABEL_COLOR`
`FILM_PAD`
`FILM_FRAME_PAD`
`FILM_FRAME_GAP`
`FILM_SPROCKET_W`
`FILM_SPROCKET_H`
`FILM_SPROCKET_R`
`FILM_SPROCKET_SPACING`
`FILM_SPROCKET_MARGIN`
`FILM_LABEL_H`

bencher.results.manim_cartesian.cartesian_product_scene

Attributes

Classes

Functions

Module Contents