Shapes

The graphical elements are divided in 4 categories:

Shapes that define the actual curves but have no styling information
Grouping, used to organize collections of graphic elements
Styles, that define the visual appearance of shapes
Modifiers alter the curves of the shapes

Shape Rendering Model

Grouping and Ordering Rules

Shapes are rendered in reverse order, bottom->top. Shapes at the beginning of the array are rendered on top of shapes with larger indices.
Groups offer a scoping mechanism for transforms, styles, modifiers, and shapes. All group children, including sub-groups and their children, are considered part of the group's scope.
Transforms adjust the coordinate system for all elements within their group, and transitively for all other group-nested elements.
Styles and modifiers apply to all preceding shapes within the current scope, including subgroup-nested shapes.
When multiple styles apply to the same shape, the shape is rendered repeatedly for each style, in reverse order.
When multiple modifiers apply to the same shape, they are composed in reverse order (e.g. $T r i m (T r i m (s h a p e))$ ).
When multiple transforms apply to the same shape due to scope nesting, they compose in group nesting order (transforms are additive).
Group opacity (property of the group transform) applies atomically to all elements in scope - i.e. opacity applies to the result of compositing all group content, and not to individual elements.

More formally:

for each $(s h a p e, s t y l e)$ tuple, where $I n d e x (s h a p e) < I n d e x (s t y l e)$ and $s h a p e \in S c o p e (s t y l e)$ :
for each modifier, in increasing index order, where Index(shape)<Index(modifier) and shape∈Scope(modifier):
- $s h a p e = m o d i f i e r (s h a p e)$
compute the total shape transformation by composing all transforms within the shape scope chain: $T_{s h a p e} = \prod_{n = 0}^{S c o p e (s h a p e)} T r a n s f o r m (s c o p e_{n})$
compute the total style transformation by composing all transforms within the style scope chain: $T_{s t y l e} = \prod_{n = 0}^{S c o p e (s t y l e)} T r a n s f o r m (s c o p e_{n})$
$R e n d e r (s h a p e \times T_{s h a p e}, s t y l e \times T_{s t y l e})$

Notes

Certain modifier operations (e.g. sequential $T r i m$ ) may require information about shapes from different groups, thus $R e n d e r ()$ calls cannot always be issued based on single-pass local knowledge.
Transforms can affect both shapes and styles (e.g. stroke width). For a given $(s h a p e, s t y l e)$ , the shape and style transforms are not necessarily equal.
Shapes without an applicable style are not rendered.
This rendering model is based on AfterEffects' Shape Layer semantics.

Rendering Convention

Shapes defined in this section contain rendering instructions. These instructions are used to generate the path as a bezier curve.

Implementations MAY use different algorithms or primitives to render the shapes but the result MUST be equivalent to the paths defined here.

Some instructions define named values for clarity and illustrative purposes, implementations are not required to have them explicitly defined in their rendering process.

When referencing animated properties, the rendering instruction will use the same name as in the JSON but it's assumed they refer to their value at a given point in time rather than the property itself. For Vector values, $v a l u e . x$ and $v a l u e . y$ in the instructions are equivalent to value[0] and value[1] respectively.

All paths MUST be closed unless specified otherwise in the rendering instructions.

When instructions call for an equality comparison between two values, implementations MAY consider similar values to be equal to overcome numerical instability.

Bezier Conversions

This documents includes algorithms to convert parametric shapes into bezier curves.

Implementations MAY use different implementations than the algorithms provided here but the output shape MUST be visually indistinguishable from the output of these algorithms.

Furthermore, when drawing individual shapes the stroke order and direction is not importand but implementations of Trim Path MUST follow the stroke order as defined by these algorithms.

Drawing instructions will contain the following commands:

Add vertex: Adds a vertex to the bezier shape in global coordinates
Set in tangent: Sets the cubic tangent to the last added vertex, with coordinates relative to it. If omitted, tangents MUST be $(0, 0)$ .
Set out tangent: Sets the cubic tangent from the last added vertex, with coordinates relative to it. If omitted, tangents MUST be $(0, 0)$ .

Approximating Ellipses with Cubic Bezier

An elliptical quadrant can be approximated by a cubic bezier segment with tangents of length $radius * E_t.

Where

E_{t} \approx 0.5519150244935105707435627

See this article for the math behind it.

When implementations render elliptical arcs using bezier curves, they SHOULD use this constant, a similar approximation, or elliptical arc drawing primitives.

Graphic Element

Element used to display vector data in a shape layer

Composition Diagram for Graphic Element

Attribute	Type	Title	Description
`nm`	`string`	Name	Human readable name, as seen from editors and the like
`hd`	`boolean`	Hidden	Whether the shape is hidden
`ty`	`string`	Shape Type	Shape Type

The ty property defines the specific element type based on the following values:

`ty`	Type
`'el'`	Ellipse
`'fl'`	Fill
`'gf'`	Gradient
`'gs'`	Gradient Stroke
`'gr'`	Group
`'sh'`	Path
`'sr'`	PolyStar
`'rc'`	Rectangle
`'st'`	Stroke
`'tr'`	Transform Shape
`'tm'`	Trim Path

Hidden shapes (hd: True) are ignored, and do not contribute to rendering nor modifier operations.

Shapes

Drawable shape, defines the actual shape but not the style

Composition Diagram for Shape

Attribute	Type	Title	Description
`nm`	`string`	Name	Human readable name, as seen from editors and the like
`hd`	`boolean`	Hidden	Whether the shape is hidden
`ty`	`string`	Shape Type	Shape Type
`d`	Shape Direction	Direction	Direction the shape is drawn as, mostly relevant when using trim path

Ellipse

Ellipse shape

Composition Diagram for Ellipse

Attribute	Type	Title	Description
`nm`	`string`	Name	Human readable name, as seen from editors and the like
`hd`	`boolean`	Hidden	Whether the shape is hidden
`ty`	`string` = `'el'`	Shape Type	Shape Type
`d`	Shape Direction	Direction	Direction the shape is drawn as, mostly relevant when using trim path
`p`	Position	Position	Position
`s`	Vector	Size	Size

Example

Position x	256
Position y	256
Width	256
Height	256


Ellipse
    Inputs:
         $\vec{p} \in ℝ^{2}$ 
         $\vec{s} \in ℝ^{2}$ 
    
    An ellipse is drawn from the top quadrant point going clockwise:
     $r a d i u s ≔ \frac{\vec{s}}{2}$ 
     $t a n g e n t ≔ r a d i u s \cdot E_{t}$ 
     $x ≔ \vec{p} . x$ 
     $y ≔ \vec{p} . y$ 

    Set shape closed
    Add vertex  $(x, y - r a d i u s . y)$ 
    Set in tangent  $(- t a n g e n t . x, 0)$ 
    Set out tangent  $(t a n g e n t . x, 0)$ 
    Add vertex  $(x + r a d i u s . x, y)$ 
    Set in tangent  $(0, - t a n g e n t . y)$ 
    Set out tangent  $(0, t a n g e n t . y)$ 
    Add vertex  $(x, y + r a d i u s . y)$ 
    Set in tangent  $(t a n g e n t . x, 0)$ 
    Set out tangent  $(- t a n g e n t . x, 0)$ 
    Add vertex  $(x - r a d i u s . x, y)$ 
    Set in tangent  $(0, t a n g e n t . y)$ 
    Set out tangent  $(0, - t a n g e n t . y)$


def ellipse(shape: Bezier, p: Vector2D, s: Vector2D):
    # An ellipse is drawn from the top quadrant point going clockwise:
    radius = s / 2
    tangent = radius * ELLIPSE_CONSTANT
    x = p.x
    y = p.y

    shape.closed = True
    shape.add_vertex(Vector2D(x, y - radius.y))
    shape.set_in_tangent(Vector2D(-tangent.x, 0))
    shape.set_out_tangent(Vector2D(tangent.x, 0))
    shape.add_vertex(Vector2D(x + radius.x, y))
    shape.set_in_tangent(Vector2D(0, -tangent.y))
    shape.set_out_tangent(Vector2D(0, tangent.y))
    shape.add_vertex(Vector2D(x, y + radius.y))
    shape.set_in_tangent(Vector2D(tangent.x, 0))
    shape.set_out_tangent(Vector2D(-tangent.x, 0))
    shape.add_vertex(Vector2D(x - radius.x, y))
    shape.set_in_tangent(Vector2D(0, tangent.y))
    shape.set_out_tangent(Vector2D(0, -tangent.y))


void ellipse(Bezier shape, Vector2D p, Vector2D s)
{
    // An ellipse is drawn from the top quadrant point going clockwise:
    radius = s / 2;
    tangent = radius * ELLIPSE_CONSTANT;
    x = p.x;
    y = p.y;

    shape.closed = true;
    shape.add_vertex(Vector2D(x, y - radius.y));
    shape.set_in_tangent(Vector2D(-tangent.x, 0));
    shape.set_out_tangent(Vector2D(tangent.x, 0));
    shape.add_vertex(Vector2D(x + radius.x, y));
    shape.set_in_tangent(Vector2D(0, -tangent.y));
    shape.set_out_tangent(Vector2D(0, tangent.y));
    shape.add_vertex(Vector2D(x, y + radius.y));
    shape.set_in_tangent(Vector2D(tangent.x, 0));
    shape.set_out_tangent(Vector2D(-tangent.x, 0));
    shape.add_vertex(Vector2D(x - radius.x, y));
    shape.set_in_tangent(Vector2D(0, tangent.y));
    shape.set_out_tangent(Vector2D(0, -tangent.y));
}


function ellipse(shape: Bezier, p: Vector2D, s: Vector2D) {
    // An ellipse is drawn from the top quadrant point going clockwise:
    radius = String / 2;
    tangent = radius * ELLIPSE_CONSTANT;
    x = p.x;
    y = p.y;

    shape.closed = true;
    shape.addVertex(new Vector2D(x, y - radius.y));
    shape.setInTangent(new Vector2D(-tangent.x, 0));
    shape.setOutTangent(new Vector2D(tangent.x, 0));
    shape.addVertex(new Vector2D(x + radius.x, y));
    shape.setInTangent(new Vector2D(0, -tangent.y));
    shape.setOutTangent(new Vector2D(0, tangent.y));
    shape.addVertex(new Vector2D(x, y + radius.y));
    shape.setInTangent(new Vector2D(tangent.x, 0));
    shape.setOutTangent(new Vector2D(-tangent.x, 0));
    shape.addVertex(new Vector2D(x - radius.x, y));
    shape.setInTangent(new Vector2D(0, tangent.y));
    shape.setOutTangent(new Vector2D(0, -tangent.y));
}

Implementations MAY use elliptical arcs to render an ellipse.

Ellipse rendering guide

Rectangle

A simple rectangle shape

Composition Diagram for Rectangle

Attribute	Type	Title	Description
`nm`	`string`	Name	Human readable name, as seen from editors and the like
`hd`	`boolean`	Hidden	Whether the shape is hidden
`ty`	`string` = `'rc'`	Shape Type	Shape Type
`d`	Shape Direction	Direction	Direction the shape is drawn as, mostly relevant when using trim path
`p`	Position	Position	Center of the rectangle
`s`	Vector	Size	Size
`r`	Scalar	Roundness	Rounded corners radius

Example

Position x	256
Position y	256
Width	256
Height	256
Roundness	0

Rendering algorithm:


Rectangle
    Inputs:
         $\vec{p} \in ℝ^{2}$ 
         $\vec{s} \in ℝ^{2}$ 
         $r \in ℝ$ 
    
     $l e f t ≔ \vec{p} . x - \frac{\vec{s} . x}{2}$ 
     $r i g h t ≔ \vec{p} . x + \frac{\vec{s} . x}{2}$ 
     $t o p ≔ \vec{p} . y - \frac{\vec{s} . y}{2}$ 
     $b o t t o m ≔ \vec{p} . y + \frac{\vec{s} . y}{2}$ 

    Set shape closed

    If  $r \leq 0$ 

        The rectangle is rendered from the top-right going clockwise

        Add vertex  $(r i g h t, t o p)$ 
        Add vertex  $(r i g h t, b o t t o m)$ 
        Add vertex  $(l e f t, b o t t o m)$ 
        Add vertex  $(l e f t, t o p)$ 

    Otherwise

        Rounded corners must be taken into account

         $r o u n d e d ≔ min (\frac{\vec{s} . x}{2}, \frac{\vec{s} . y}{2}, r)$ 
         $t a n g e n t ≔ r o u n d e d \cdot E_{t}$ 

        Add vertex  $(r i g h t, t o p + r o u n d e d)$ 
        Set in tangent  $(0, - t a n g e n t)$ 
        Add vertex  $(r i g h t, b o t t o m - r o u n d e d)$ 
        Set out tangent  $(0, t a n g e n t)$ 
        Add vertex  $(r i g h t - r o u n d e d, b o t t o m)$ 
        Set in tangent  $(t a n g e n t, 0)$ 
        Add vertex  $(l e f t + r o u n d e d, b o t t o m)$ 
        Set out tangent  $(- t a n g e n t, 0)$ 
        Add vertex  $(l e f t, b o t t o m - r o u n d e d)$ 
        Set in tangent  $(0, t a n g e n t)$ 
        Add vertex  $(l e f t, t o p + r o u n d e d)$ 
        Set out tangent  $(0, - t a n g e n t)$ 
        Add vertex  $(l e f t + r o u n d e d, t o p)$ 
        Set in tangent  $(- t a n g e n t, 0)$ 
        Add vertex  $(r i g h t - r o u n d e d, t o p)$ 
        Set out tangent  $(t a n g e n t, 0)$


def rectangle(shape: Bezier, p: Vector2D, s: Vector2D, r: float):
    left: float = p.x - s.x / 2
    right: float = p.x + s.x / 2
    top: float = p.y - s.y / 2
    bottom: float = p.y + s.y / 2

    shape.closed = True

    if r <= 0:

        # The rectangle is rendered from the top-right going clockwise

        shape.add_vertex(Vector2D(right, top))
        shape.add_vertex(Vector2D(right, bottom))
        shape.add_vertex(Vector2D(left, bottom))
        shape.add_vertex(Vector2D(left, top))

    else:

        # Rounded corners must be taken into account

        rounded: float = min(s.x/2, s.y/2, r)
        tangent: float = rounded * ELLIPSE_CONSTANT

        shape.add_vertex(Vector2D(right, top + rounded))
        shape.set_in_tangent(Vector2D(0, -tangent))
        shape.add_vertex(Vector2D(right, bottom - rounded))
        shape.set_out_tangent(Vector2D(0, tangent))
        shape.add_vertex(Vector2D(right - rounded, bottom))
        shape.set_in_tangent(Vector2D(tangent, 0))
        shape.add_vertex(Vector2D(left + rounded, bottom))
        shape.set_out_tangent(Vector2D(-tangent, 0))
        shape.add_vertex(Vector2D(left, bottom - rounded))
        shape.set_in_tangent(Vector2D(0, tangent))
        shape.add_vertex(Vector2D(left, top + rounded))
        shape.set_out_tangent(Vector2D(0, -tangent))
        shape.add_vertex(Vector2D(left + rounded, top))
        shape.set_in_tangent(Vector2D(-tangent, 0))
        shape.add_vertex(Vector2D(right - rounded, top))
        shape.set_out_tangent(Vector2D(tangent, 0))


void rectangle(Bezier shape, Vector2D p, Vector2D s, float r)
{
    float left = p.x - s.x / 2;
    float right = p.x + s.x / 2;
    float top = p.y - s.y / 2;
    float bottom = p.y + s.y / 2;

    shape.closed = true;

    if ( r <= 0 )
    {
        // The rectangle is rendered from the top-right going clockwise

        shape.add_vertex(Vector2D(right, top));
        shape.add_vertex(Vector2D(right, bottom));
        shape.add_vertex(Vector2D(left, bottom));
        shape.add_vertex(Vector2D(left, top));
    }
    // Rounded corners must be taken into account

    else
    {
        float rounded = std::min(s.x / 2, s.y / 2, r);
        float tangent = rounded * ELLIPSE_CONSTANT;

        shape.add_vertex(Vector2D(right, top + rounded));
        shape.set_in_tangent(Vector2D(0, -tangent));
        shape.add_vertex(Vector2D(right, bottom - rounded));
        shape.set_out_tangent(Vector2D(0, tangent));
        shape.add_vertex(Vector2D(right - rounded, bottom));
        shape.set_in_tangent(Vector2D(tangent, 0));
        shape.add_vertex(Vector2D(left + rounded, bottom));
        shape.set_out_tangent(Vector2D(-tangent, 0));
        shape.add_vertex(Vector2D(left, bottom - rounded));
        shape.set_in_tangent(Vector2D(0, tangent));
        shape.add_vertex(Vector2D(left, top + rounded));
        shape.set_out_tangent(Vector2D(0, -tangent));
        shape.add_vertex(Vector2D(left + rounded, top));
        shape.set_in_tangent(Vector2D(-tangent, 0));
        shape.add_vertex(Vector2D(right - rounded, top));
        shape.set_out_tangent(Vector2D(tangent, 0));
    }
}


function rectangle(shape: Bezier, p: Vector2D, s: Vector2D, r: number) {
    let left: number = p.x - String.x / 2;
    let right: number = p.x + String.x / 2;
    let top: number = p.y - String.y / 2;
    let bottom: number = p.y + String.y / 2;

    shape.closed = true;

    if ( String <= 0 ) {

        // The rectangle is rendered from the top-right going clockwise

        shape.addVertex(new Vector2D(right, top));
        shape.addVertex(new Vector2D(right, bottom));
        shape.addVertex(new Vector2D(left, bottom));
        shape.addVertex(new Vector2D(left, top));

    } else {

        // Rounded corners must be taken into account

        let rounded: number = Math.min(String.x / 2, String.y / 2, String);
        let tangent: number = rounded * ELLIPSE_CONSTANT;

        shape.addVertex(new Vector2D(right, top + rounded));
        shape.setInTangent(new Vector2D(0, -tangent));
        shape.addVertex(new Vector2D(right, bottom - rounded));
        shape.setOutTangent(new Vector2D(0, tangent));
        shape.addVertex(new Vector2D(right - rounded, bottom));
        shape.setInTangent(new Vector2D(tangent, 0));
        shape.addVertex(new Vector2D(left + rounded, bottom));
        shape.setOutTangent(new Vector2D(-tangent, 0));
        shape.addVertex(new Vector2D(left, bottom - rounded));
        shape.setInTangent(new Vector2D(0, tangent));
        shape.addVertex(new Vector2D(left, top + rounded));
        shape.setOutTangent(new Vector2D(0, -tangent));
        shape.addVertex(new Vector2D(left + rounded, top));
        shape.setInTangent(new Vector2D(-tangent, 0));
        shape.addVertex(new Vector2D(right - rounded, top));
        shape.setOutTangent(new Vector2D(tangent, 0));
    }
}

Rectangle rendering guide

Path

Custom Bezier shape

Composition Diagram for Path

Attribute	Type	Title	Description
`nm`	`string`	Name	Human readable name, as seen from editors and the like
`hd`	`boolean`	Hidden	Whether the shape is hidden
`ty`	`string` = `'sh'`	Shape Type	Shape Type
`d`	Shape Direction	Direction	Direction the shape is drawn as, mostly relevant when using trim path
`ks`	Bezier	Shape	Bezier path

Example

Shape 

PolyStar

Star or regular polygon

Composition Diagram for PolyStar

Attribute	Type	Title	Description
`nm`	`string`	Name	Human readable name, as seen from editors and the like
`hd`	`boolean`	Hidden	Whether the shape is hidden
`ty`	`string` = `'sr'`	Shape Type	Shape Type
`d`	Shape Direction	Direction	Direction the shape is drawn as, mostly relevant when using trim path
`p`	Position	Position	Position
`or`	Scalar	Outer Radius	Outer Radius
`os`	Scalar	Outer Roundness	Outer Roundness as a percentage
`r`	Scalar	Rotation	Rotation, clockwise in degrees
`pt`	Scalar	Points	Points
`sy`	Star Type	Star Type	Star Type
`ir`	Scalar	Inner Radius	Inner Radius
`is`	Scalar	Inner Roundness	Inner Roundness as a percentage

Example

Position x	256
Position y	256
Points	5
Rotation	0
Outer Radius	200
Inner Radius	100
Outer Roundness	0
Inner Roundness	0
Star Type


Polystar
    Inputs:
         $\vec{p} \in ℝ^{2}$ 
         $p t \in ℝ$ 
         $r \in ℝ$ 
         $o r \in ℝ$ 
         $o s \in ℝ$ 
         $s y \in ℤ$ 
         $i r \in ℝ$ 
         $i s \in ℝ$ 
    
     $p o i n t s ≔ ⌊ p t ⌉$ 
     $α ≔ \frac{- r \cdot π}{180} - \frac{π}{2}$ 
     $θ ≔ \frac{- π}{p o i n t s}$ 
     $t a n L e n_{o u t} ≔ \frac{2 \cdot π \cdot o r}{4 \cdot p o i n t s} \cdot \frac{o s}{100}$ 
     $t a n L e n_{i n} ≔ \frac{2 \cdot π \cdot i r}{4 \cdot p o i n t s} \cdot \frac{i s}{100}$ 

    Set shape closed

    For each  $i$  in  $[0, p o i n t s)$ 
         $β ≔ α + i \cdot θ \cdot 2$ 
         $\vec{v_{o u t}} ≔ (o r \cdot \cos (β), o r \cdot \sin (β))$ 
        Add vertex  $\vec{p} + \vec{v_{o u t}}$ 

        If  $o s \neq 0 \land o r \neq 0$ 
            We need to add bezier tangents
             $\vec{t a n_{o u t}} ≔ \frac{\vec{v_{o u t}} \cdot t a n L e n_{o u t}}{o r}$ 
            Set in tangent  $(- \vec{t a n_{o u t}} . y, \vec{t a n_{o u t}} . x)$ 
            Set out tangent  $(\vec{t a n_{o u t}} . y, - \vec{t a n_{o u t}} . x)$ 

        If  $s y = 1$ 
            We need to add a vertex towards the inner radius to make a star
             $\vec{v_{i n}} ≔ (i r \cdot \cos (β + θ), i r \cdot \sin (β + θ))$ 
            Add vertex  $\vec{p} + \vec{v_{i n}}$ 

            If  $i s \neq 0 \land i r \neq 0$ 
                We need to add bezier tangents
                 $t a n_{i n} ≔ \frac{\vec{v_{i n}} \cdot t a n L e n_{i n}}{i r}$ 
                Set in tangent  $(- t a n_{i n} . y, t a n_{i n} . x)$ 
                Set out tangent  $(t a n_{i n} . y, - t a n_{i n} . x)$


def polystar(shape: Bezier, p: Vector2D, pt: float, r: float, or_: float, os: float, sy: int, ir: float, is_: float):
    points: int = int(round(pt))
    alpha: float = -r * math.pi / 180 - math.pi / 2
    theta: float = -math.pi / points
    tan_len_out: float = (2 * math.pi * or_) / (4 * points) * (os / 100)
    tan_len_in: float = (2 * math.pi * ir) / (4 * points) * (is_ / 100)

    shape.closed = True

    for i in range(points):
        beta: float = alpha + i * theta * 2
        v_out: Vector2D = Vector2D(or_ * math.cos(beta),  or_ * math.sin(beta))
        shape.add_vertex(p + v_out)

        if os != 0 and or_ != 0:
            # We need to add bezier tangents
            tan_out: Vector2D = v_out * tan_len_out / or_
            shape.set_in_tangent(Vector2D(-tan_out.y, tan_out.x))
            shape.set_out_tangent(Vector2D(tan_out.y, -tan_out.x))

        if sy == 1:
            # We need to add a vertex towards the inner radius to make a star
            v_in: Vector2D = Vector2D(ir * math.cos(beta + theta), ir * math.sin(beta + theta))
            shape.add_vertex(p + v_in)

            if is_ != 0 and ir != 0:
                # We need to add bezier tangents
                tan_in = v_in * tan_len_in / ir
                shape.set_in_tangent(Vector2D(-tan_in.y, tan_in.x))
                shape.set_out_tangent(Vector2D(tan_in.y, -tan_in.x))


void polystar(Bezier shape, Vector2D p, float pt, float r, float or_, float os, int sy, float ir, float is)
{
    int points = std::round(pt);
    float alpha = -r * std::numbers::pi / 180 - std::numbers::pi / 2;
    float theta = -std::numbers::pi / points;
    float tan_len_out = 2 * std::numbers::pi * or_ / 4 * points * os / 100;
    float tan_len_in = 2 * std::numbers::pi * ir / 4 * points * is / 100;

    shape.closed = true;

    for ( int i = 0; i < points; i++ )
    {
        float beta = alpha + i * theta * 2;
        Vector2D v_out(or_ * std::cos(beta), or_ * std::sin(beta));
        shape.add_vertex(p + v_out);

        if ( os != 0 && or_ != 0 )
        {
            // We need to add bezier tangents
            Vector2D tan_out = v_out * tan_len_out / or_;
            shape.set_in_tangent(Vector2D(-tan_out.y, tan_out.x));
            shape.set_out_tangent(Vector2D(tan_out.y, -tan_out.x));
        }

        if ( sy == 1 )
        {
            // We need to add a vertex towards the inner radius to make a star
            Vector2D v_in(ir * std::cos(beta + theta), ir * std::sin(beta + theta));
            shape.add_vertex(p + v_in);

            if ( is != 0 && ir != 0 )
            {
                // We need to add bezier tangents
                tan_in = v_in * tan_len_in / ir;
                shape.set_in_tangent(Vector2D(-tan_in.y, tan_in.x));
                shape.set_out_tangent(Vector2D(tan_in.y, -tan_in.x));
            }
        }
    }
}


function polystar(shape: Bezier, p: Vector2D, pt: number, r: number, or: number, os: number, sy: number, ir: number, is: number) {
    let points: number = new Number(round(pt));
    let alpha: number = -String * Math.PI / 180 - Math.PI / 2;
    let theta: number = -Math.PI / points;
    let tanLenOut: number = 2 * Math.PI * or / 4 * points * os / 100;
    let tanLenIn: number = 2 * Math.PI * ir / 4 * points * is / 100;

    shape.closed = true;

    for ( let i: number = 0; i < points; i++ ) {
        let beta: number = alpha + i * theta * 2;
        let vOut: Vector2D = new Vector2D(or * Math.cos(beta), or * Math.sin(beta));
        shape.addVertex(p + vOut);

        if ( os != 0 && or != 0 ) {
            // We need to add bezier tangents
            let tanOut: Vector2D = vOut * tanLenOut / or;
            shape.setInTangent(new Vector2D(-tanOut.y, tanOut.x));
            shape.setOutTangent(new Vector2D(tanOut.y, -tanOut.x));
        }

        if ( sy == 1 ) {
            // We need to add a vertex towards the inner radius to make a star
            let vIn: Vector2D = new Vector2D(ir * Math.cos(beta + theta), ir * Math.sin(beta + theta));
            shape.addVertex(p + vIn);

            if ( is != 0 && ir != 0 ) {
                // We need to add bezier tangents
                tanIn = vIn * tanLenIn / ir;
                shape.setInTangent(new Vector2D(-tanIn.y, tanIn.x));
                shape.setOutTangent(new Vector2D(tanIn.y, -tanIn.x));
            }
        }
    }
}

Grouping

Group

Shape Element that can contain other shapes

Composition Diagram for Group

Attribute	Type	Title	Description
`nm`	`string`	Name	Human readable name, as seen from editors and the like
`hd`	`boolean`	Hidden	Whether the shape is hidden
`ty`	`string` = `'gr'`	Shape Type	Shape Type
`np`	`number`	Number Of Properties	Number Of Properties
`it`	`array` of Graphic Element	Shapes	Shapes

A group defines a render stack, elements within a group MUST be rendered in reverse order (the first object in the list will appear on top of elements further down).

Apply the transform
Render Styles and child groups in the transformed coordinate system.

Transform

Group transform

Composition Diagram for Transform Shape

Attribute	Type	Title	Description
`nm`	`string`	Name	Human readable name, as seen from editors and the like
`hd`	`boolean`	Hidden	Whether the shape is hidden
`ty`	`string` = `'tr'`	Shape Type	Shape Type
`a`	Position	Anchor Point	Anchor point: a position (relative to its parent) around which transformations are applied (ie: center for rotation / scale)
`p`	Splittable Position	Position	Position / Translation
`r`	Scalar	Rotation	Rotation in degrees, clockwise
`s`	Vector	Scale	Scale factor, `[100, 100]` for no scaling
`o`	Scalar	Opacity	Opacity
`sk`	Scalar	Skew	Skew amount as an angle in degrees
`sa`	Scalar	Skew Axis	Direction along which skew is applied, in degrees (`0` skews along the X axis, `90` along the Y axis)

Transform shapes MUST always be present in the group and they MUST be the last item in the it array.

They modify the group's coordinate system the same way as Layer Transform.

Style

Describes the visual appearance (like fill and stroke) of neighbouring shapes

Composition Diagram for Shape Style

Attribute	Type	Title	Description
`nm`	`string`	Name	Human readable name, as seen from editors and the like
`hd`	`boolean`	Hidden	Whether the shape is hidden
`ty`	`string`	Shape Type	Shape Type
`o`	Scalar	Opacity	Opacity, 100 means fully opaque

Shapes styles MUST apply their style to the collected shapes that come before them in stacking order.

Fill

Solid fill color

Composition Diagram for Fill

Attribute	Type	Title	Description
`nm`	`string`	Name	Human readable name, as seen from editors and the like
`hd`	`boolean`	Hidden	Whether the shape is hidden
`ty`	`string` = `'fl'`	Shape Type	Shape Type
`o`	Scalar	Opacity	Opacity, 100 means fully opaque
`c`	Color	Color	Color
`r`	Fill Rule	Fill Rule	Fill Rule

Example

Red	1
Green	0.98
Blue	0.28
Opacity	100
Fill Rule

Stroke

Solid stroke

Composition Diagram for Stroke

Attribute	Type	Title	Description
`nm`	`string`	Name	Human readable name, as seen from editors and the like
`hd`	`boolean`	Hidden	Whether the shape is hidden
`ty`	`string` = `'st'`	Shape Type	Shape Type
`o`	Scalar	Opacity	Opacity, 100 means fully opaque
`lc`	Line Cap	Line Cap	Line Cap
`lj`	Line Join	Line Join	Line Join
`ml`	`number`	Miter Limit	Miter Limit
`ml2`	Scalar	Miter Limit	Animatable alternative to ml
`w`	Scalar	Width	Stroke width
`d`	`array` of Stroke Dash	Dashes	Dashed line definition
`c`	Color	Color	Stroke color

Example

Red	1
Green	0.98
Blue	0.28
Width	32
Opacity	100
Line Cap
Line Join
Miter Limit	3

Stroke Dashes

An item used to described the dash pattern in a stroked path

A stroke dash array consists of n dash entries, [n-1,n] gap entries and [0-1] offset entries.

Dash and gap entries MUST all be in a continuous order and alternate between dash and gap, starting with dash. If there are an odd number of dashes + gaps, the sequence will repeat with dashes and gaps reversed. For example a sequence of [4d, 8g, 16d] MUST be rendered as [4d, 8g, 16d, 4g, 8d, 16g].

Offset entry, if present, MUST be at the end of the array.

Composition Diagram for Stroke Dash

Attribute	Type	Title	Description
`nm`	`string`	Name	Human readable name, as seen from editors and the like
`n`	Stroke Dash Type	Dash Type	Dash Type
`v`	Scalar	Length	Length of the dash

Example

Red	1
Green	0.98
Blue	0.28
Width	32
Opacity	100
Line Cap
Line Join
Miter Limit	3
Dash Offset	0
Dash Length	30
Dash Gap	50

Gradient Fill

Gradient fill color

Composition Diagram for Gradient

Attribute	Type	Title	Description
`nm`	`string`	Name	Human readable name, as seen from editors and the like
`hd`	`boolean`	Hidden	Whether the shape is hidden
`ty`	`string` = `'gf'`	Shape Type	Shape Type
`o`	Scalar	Opacity	Opacity, 100 means fully opaque
`g`	Gradient	Colors	Gradient colors
`s`	Position	Start Point	Starting point for the gradient
`e`	Position	End Point	End point for the gradient
`t`	Gradient Type	Gradient Type	Type of the gradient
`h`	Scalar	Highlight Length	Highlight Length, as a percentage between `s` and `e`
`a`	Scalar	Highlight Angle	Highlight Angle in clockwise degrees, relative to the direction from `s` to `e`
`r`	Fill Rule	Fill Rule	Fill Rule

Example

Start X	256
Start Y	496
End X	256
End Y	16
Type
Highlight	0
Highlight Angle	0

Gradient Stroke

Gradient stroke

Composition Diagram for Gradient Stroke

Attribute	Type	Title	Description
`nm`	`string`	Name	Human readable name, as seen from editors and the like
`hd`	`boolean`	Hidden	Whether the shape is hidden
`ty`	`string` = `'gs'`	Shape Type	Shape Type
`o`	Scalar	Opacity	Opacity, 100 means fully opaque
`lc`	Line Cap	Line Cap	Line Cap
`lj`	Line Join	Line Join	Line Join
`ml`	`number`	Miter Limit	Miter Limit
`ml2`	Scalar	Miter Limit	Animatable alternative to ml
`w`	Scalar	Width	Stroke width
`d`	`array` of Stroke Dash	Dashes	Dashed line definition
`g`	Gradient	Colors	Gradient colors
`s`	Position	Start Point	Starting point for the gradient
`e`	Position	End Point	End point for the gradient
`t`	Gradient Type	Gradient Type	Type of the gradient
`h`	Scalar	Highlight Length	Highlight Length, as a percentage between `s` and `e`
`a`	Scalar	Highlight Angle	Highlight Angle in clockwise degrees, relative to the direction from `s` to `e`

Example

Start X	256
Start Y	496
End X	256
End Y	16
Type
Highlight	0
Highlight Angle	0

Modifiers

Modifiers change the bezier curves of neighbouring shapes

Modifiers replace shapes in the render stack by applying operating on the bezier path of to the collected shapes that come before it in stacking order.

Trim Path

Trims shapes into a segment

Composition Diagram for Trim Path

Attribute	Type	Title	Description
`nm`	`string`	Name	Human readable name, as seen from editors and the like
`hd`	`boolean`	Hidden	Whether the shape is hidden
`ty`	`string` = `'tm'`	Shape Type	Shape Type
`s`	Scalar	Start	Segment start
`e`	Scalar	End	Segment end
`o`	Scalar	Offset	Offset
`m`	Trim Multiple Shapes	Multiple	How to treat multiple copies

Start	0
End	50
Offset	0
Multiple Shapes

When rendering trim path, the order of bezier points MUST be the same as rendering instructions given for each shape in this section.

Rendering trim path can be rather complex.

Given

\begin{matrix} o f f s e t & = {\begin{matrix} \frac{o}{360} - ⌊ \frac{o}{360} ⌋ & o \geq 0 \\ \frac{o}{360} - ⌈ \frac{o}{360} ⌉ & o < 0 \end{matrix} \\ s t a r t & = o f f s e t + min (1, max (0, \frac{min (s, e)}{100})) \\ e n d & = o f f s e t + min (1, max (0, \frac{max (s, e)}{100})) \end{matrix}

If $s$ and $e$ are equal, implementations MUST NOT render any shapes.

If $s = 0$ and $e = 1$ , the input shape MUST be rendered as-is.

To render trim path, implementations MUST consider the actual length of each shape (they MAY use approximations). Once the shapes are collected, the segment to render is given by the percentages $s t a r t$ and $e n d$ .

When trim path is applied to multiple shapes, the m property MUST be considered when applying the modifier:

When m has a value of 1 (Parallel), each shape MUST be considered separately, $s t a r t$ and $e n d$ being applied to each shape.
When m has a value of 2 (Sequential), all the shapes MUST be considered as following each other in render order. $s t a r t$ and $e n d$ refer to the whole length created by concatenating each shape.

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