LinearTransform and VectorSum

Cargo featurefeatures = ["math"]

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LinearTransform is Manim’s ApplyMatrix on a LinearTransformationScene. It moves a grid and the two basis vectors from the identity to matrix over run_time, over the original grid drawn faintly, and writes the matrix at matrix_at with the Matrix component. VectorSum adds vectors tip to tail: each one moves from origin to the tip of the one before, then the resultant draws with resultant_enter. apply(m, p) and towards(m, p) are the matrix product and the interpolation from the identity they use. Gallery scenes: LinearTransform, VectorSum.

LinearTransform demo, first frame — `LinearTransform` 4 s

VectorSum demo, first frame — `VectorSum` 4.5 s

use fframes_kit::prelude::*;
use fframes_kit::kits::math::apply;

fn figure<'a>(ui: &mut Ui<'a, '_, '_>) -> Svgr<'a> {
    let shear = ui.show(LinearTransform {
        matrix: [[1.0, 1.0], [0.0, 1.0]],
        delay: 1.0,
        ..ui.defaults()
    });
    let sum = ui.show(VectorSum {
        vectors: vec![(3.0, 1.0), (1.0, 2.0)],
        labels: vec!["u".into(), "v".into()],
        resultant_label: "u + v".into(),
        delay: 3.5,
        resultant_enter: Some(Create { delay: 5.0, ..Create::default() }.into()),
        resultant_label_enter: Some(FadeIn { delay: 5.5, ..FadeIn::default() }),
        ..ui.defaults()
    });
    svgr!(<g>{shear}{sum}</g>)
}

assert_eq!(apply([[1.0, 1.0], [0.0, 1.0]], (2.0, 3.0)), (5.0, 3.0));

API

Components are plain structs. Set the fields you need and fill the rest with ..ui.defaults(): the defaults below come from the current theme (theme. values are fields of Theme).

LinearTransform

A grid of lines and the two basis vectors moved by matrix (Manim’s LinearTransformationScene with ApplyMatrix): from the identity to the matrix over run_time seconds after delay, over the untransformed grid drawn faintly. The grid has a line at every integer of x_range and y_range, in units of ui.space around center, and the moved grid is clipped to its box; key tells the clip paths of two transforms apart. With show_matrix the matrix is written at matrix_at (pixels).

Field	Type	Default	Description
`matrix`	`Mat2`	`[[1.0, 1.0], [0.0, 1.0]]`	The 2x2 matrix to apply, row by row; its columns are where the basis vectors `i` and `j` end up.
`x_range`	`Range`	`Range::new(-4.0, 4.0, 1.0)`	The grid’s x extent in units of `ui.space` from `center`, with a vertical line at every tick.
`y_range`	`Range`	`Range::new(-3.0, 3.0, 1.0)`	The grid’s y extent in units of `ui.space` from `center`, with a horizontal line at every tick.
`center`	`(f64, f64)`	`(0.0, 0.0)`	Where the grid’s origin sits, in units of `ui.space` (y up).
`delay`	`f32`	`0.0`	Seconds after the container’s start before the transformation begins.
`run_time`	`f32`	`2.0`	Seconds the grid takes to move from the identity to `matrix`.
`rate_func`	`RateFunc`	`RateFunc::default()`	Easing of the movement over its run time.
`line_color`	`Color`	`theme.colors.accent`	Colour of the moving grid lines; the untransformed grid is drawn faintly in the muted colour.
`stroke_width`	`f32`	`theme.stroke.thin`	Grid line width in pixels.
`i_color`	`Color`	`theme.colors.highlight`	Colour of the basis vector `i` (to `(1, 0)`).
`j_color`	`Color`	`theme.colors.caption`	Colour of the basis vector `j` (to `(0, 1)`).
`show_matrix`	`bool`	`true`	Writes `matrix` at `matrix_at` when `true`.
`matrix_at`	`(f32, f32)`	`(1600.0, 200.0)`	Where the written matrix sits, in pixels of the canvas.
`enter`	`Option<EnterAnim>`	`None`	How the grids and the vectors appear.
`matrix_enter`	`Option<FadeIn>`	`Some(FadeIn::themed(theme))`	Fade in of the written matrix’s entries; `None` shows them from the start.
`key`	`Option<&str>`	`None`	Names the clip path when two transforms share a frame; `None` for the default.

Feature math · Source

VectorSum

Vectors added tip to tail (Manim’s vector addition): every vector starts at origin, then moves over run_time seconds after delay to the tip of the one before, and the resultant from origin to the last tip draws with resultant_enter (a Create delayed past the move). Vectors are in units of ui.space; labels are written at the middle of the vectors, on their left, and resultant_label on the side of the resultant away from them.

Field	Type	Default	Description
`vectors`	`Vec<(f64, f64)>`	`Vec::new()`	The vectors `(dx, dy)` in units of `ui.space` (y up), added in order tip to tail.
`origin`	`(f64, f64)`	`(0.0, 0.0)`	Where the first vector starts and the resultant begins, in units of `ui.space`.
`colors`	`Vec<Color>`	`Vec::new()`	Colours of the vectors in turn; empty for the theme’s accent and highlight.
`labels`	`Vec<Cow<str>>`	`Vec::new()`	Text for each vector in turn, written at its middle; a vector without one has none.
`delay`	`f32`	`0.0`	Seconds after the container’s start before the vectors begin to move into place.
`run_time`	`f32`	`1.5`	Seconds the vectors take to move to the tip of the one before.
`rate_func`	`RateFunc`	`RateFunc::default()`	Easing of the move over its run time.
`resultant`	`bool`	`true`	Draws the sum from `origin` to the last tip when `true`.
`resultant_color`	`Color`	`theme.colors.title`	Colour of the resultant.
`resultant_label`	`Cow<str>`	`Cow::Borrowed("")`	Text written beside the resultant; empty for none.
`enter`	`Option<EnterAnim>`	`None`	How each vector appears; `None` shows them from the start.
`resultant_enter`	`Option<EnterAnim>`	`None`	How the resultant appears; `None` shows it from the start.
`labels_enter`	`Option<FadeIn>`	`None`	Fade in of the vector labels; `None` for none.
`resultant_label_enter`	`Option<FadeIn>`	`None`	The resultant’s label also fades with this, to wait for the resultant.

Methods:

fn total(&self) -> (f64, f64): The sum of the vectors.

Feature math · Source