SVG paths are defined with the <path> element and can describe virtually any shape using a series of commands. A path's d attribute contains these commands, starting with move commands (M or m), line commands (L, l, H, h, V, v), curve commands (C, c, S, s, Q, q, T, t), arc commands (A, a), and closepath commands (Z or z).

Here's an example of a simple path:

<svg width="200" height="200" xmlns="http://www.w3.org/2000/svg">
  <path d="M10 10 H 190 V 190 H 10 Z" fill="transparent" stroke="cyan" stroke-width="2"/>
</svg>

This path starts at point (10,10) within the container, draws a horizontal line to (190,10), a vertical line to (190,190), a horizontal line back to (10,190), and finally closes the shape back at (10,10), forming a square.

Command by command:

- M10 10: Move to (10,10).

- H 190: Draw a horizontal line to x=190 from the current y-position.

- V 190: Draw a vertical line to y=190 from the current x-position.

- H 10: Draw a horizontal line back to x=10.

- Z: Close the path by connecting the last point to the first point.

Further understanding the SVG path:

The d attribute in an SVG <path> element is a mini language within itself, designed to define the shape of the path. It's composed of a series of commands and parameters that instruct how the path should be drawn. Let's break down the basics and how the numbers work within these commands.

Basic Commands in the d Attribute:

- M (moveto): Moves the pen to a new location. Syntax: M x,y or m dx,dy. The uppercase M moves to an absolute position, while the lowercase m moves to a position relative to the current position.

- L (lineto): Draws a straight line from the current position to a new position. Syntax: L x,y or l dx,dy. Like M, uppercase means absolute positioning, lowercase means relative.

- H (horizontal lineto): Draws a horizontal line from the current position. Syntax: H x or h dx. Uppercase means the line will go to an absolute x-coordinate, lowercase means it will move a relative distance from the current position.

- V (vertical lineto): Draws a vertical line from the current position. Syntax: V y or v dy. Uppercase means the line will go to an absolute y-coordinate, lowercase means a relative move.

- C (curveto) : Draws a cubic Bézier curve from the current point to a new point. Syntax: C x1,y1 x2,y2 x,y or c dx1,dy1 dx2,dy2 dx,dy. The points (x1,y1) and(x2,y2) are control points for the curve, and (x,y) is the end point of the curve.

- S (smooth curveto): Similar to C, but assumes the first control point is a reflection of the last control point from the previous C or S command. Useful for chaining Bézier curves. Syntax: S x2,y2 x,y or s dx2,dy2 dx,dy.

- Q (quadratic Bézier curveto): Draws a quadratic Bézier curve. Syntax: Q x1,y1 x,y or q dx1,dy1 dx,dy, where (x1,y1) is the control point.

- T (smooth quadratic Bézier curveto): Like Q, but assumes the control point is a reflection of the last control point from the previous Q or T command.

- A (elliptical Arc): Draws an arc of an ellipse. Syntax:A rx,ry rotation large-arc-flag,sweep-flag x,y or a drx,dry rotation large-arc-flag, sweep-flag dx,dy.

- Z (closepath): Closes the path by drawing a straight line back to where the current path started.

Understanding the Numbers and Parameters

Each command is followed by parameters that define the specifics of the shape to be drawn. These parameters are typically coordinates (x,y) or distances (dx,dy) and control points for curves. The difference between absolute commands (M, L, C, etc.) and relative commands (m, l, c, etc.) is that absolute commands specify a location or distance from the origin (0,0) of the SVG canvas, while relative commands specify a location or distance from the current point.

The numbers specified in SVG path commands, as well as other SVG elements' attributes like width, height, coordinates (such as cx,cy for circles, or x, y for rectangles), are in pixel units by default when no unit is specified. This means that when you define a path or set the dimensions and positions of SVG elements using these numbers, you're essentially specifying pixels as the unit of measurement relative to the SVG canvas' coordinate system.

SVG Units and Coordinates

Pixel Units: In the context of SVGs embedded in HTML documents or standalone SVG files viewed in a browser, the default unit of measurement is pixels. For example, M10 10 L90 90 moves to (10,10) pixels from the origin (top-left corner) and draws a line to (90,90) pixels.

Viewport Units: SVGs can also use viewport-relative units like vw (viewport width) and vh (viewport height), among others, which can be useful for responsive designs. However, these units are typically used in style sheets or attributes like width and height on the <svg> element itself, rather than within the d attribute of a <path>.

SVG Scalability

Despite the use of pixel units for simplicity and clarity, one of the strengths of SVG (Scalable Vector Graphics) is that the graphics are not rendered as pixels directly but as scalable vector paths. This means they remain crisp and clear at any size or zoom level, without the pixelation that can occur with bitmap images (like JPEGs or PNGs) when they are scaled up.

When designing SVG graphics and animations, it's important to consider the context in which they will be used, including the size and scalability of the graphics, especially if you're integrating the SVG into a responsive web design.

<svg width="40vh" height="40vh" 
  viewBox="0 0 100 100" xmlns="http://www.w3.org/2000/svg">
  <path d="M10,10 L90,10 L90,90 L10,90 Z" fill="deeppink" stroke="cyan" strokeWidth="0.1vh"/>
</svg>

SVG path commands within the d attribute typically use coordinate values that do not directly support viewport units like vh (viewport height) or vw (viewport width), because these commands are interpreted in the SVG's own coordinate system, which defaults to pixels. However, you can design an SVG's overall dimensions using vh and vw to make the SVG container responsive, and then draw paths within this responsive container.

Although the d attribute itself doesn't use vh or vw, the effect of using viewport units on the SVG element can be demonstrated by scaling the SVG container. Here's how you can create a responsive SVG that scales with the viewport, with a path inside.

SVG Container: The width and height of the SVG are set to 40vw and 40vh, respectively. This means the SVG will take up 40% of the viewport height in both direcitons, making it responsive to the size of the viewport.

viewBox Attribute: The viewBox attribute is set to 0 0 100 100, which defines the coordinate system used inside the SVG. This allows the path inside to scale fluidly within the SVG container. The viewBox makes it possible to define paths using "virtual" pixels that scale with the container, rather than directly using vh or vw in the path data.

Path Command: The path command draws a square within this coordinate system. Regardless of the actual size of the SVG on the screen (which scales with the viewport because of vw and vh), the path coordinates are defined in terms of the viewBox dimensions, allowing the path to scale proportionally within the SVG container.

By using vw and vh on the SVG element and a suitable viewBox, you can create scalable vector graphics that adapt to the viewport size, with paths that automatically resize to fit the container. This approach maintains the scalability and responsiveness of SVG graphics on different screen sizes, ensuring your graphics look great on any device.

The viewBox attribute

The viewBox attribute in an SVG element is a critical feature for creating scalable graphics. It defines the aspect ratio and the portion of the canvas to be displayed. The viewBox attribute consists of four space-separated values:

<svg viewBox="min-x min-y width height">

- min-x: The x-coordinate of the top-left corner of the viewBox.

- min-y: The y-coordinate of the top-left corner of the viewBox.

- width: The width of the viewBox.

- height: The height of the viewBox.

The viewBox attribute defines the coordinate system used within the SVG, allowing you to define paths and other elements using these coordinates. This makes it possible to create graphics that scale fluidly with the size of the SVG container, ensuring they look great on any device.

Adjusting the viewBox and SVG Content Coordinates

Centering an SVG animation (or any SVG content) within its container or the viewBox involves understanding how the SVG coordinate system works and using it to your advantage. There are two main strategies to consider.

If your animation or graphic is not centered in the SVG canvas, you can adjust the viewBox and the coordinates of your SVG content to center it. The viewBox attribute creates a virtual canvas, allowing you to control which part of the SVG content is visible and how it's scaled.

- Understand Your Content's Dimensions: Determine the width and height of the content you want to center.

- Adjust viewBox Accordingly: Set the viewBox such that your content is centered within this virtual canvas. This might involve changing the minX and minY values to shift the visible area.

<svg width="200px" height="200px" viewBox="-50 -50 200 200" xmlns="http://www.w3.org/2000/svg">
  <!-- Your centered content here -->
</svg>

Centering SVG content involves understanding both the SVG coordinate system (via the viewBox) and CSS layout techniques. Adjusting the viewBox can center content within the SVG canvas, while CSS or SVG transformations (e.g., transform: translate) can help center the SVG within its container or elements within the SVG. The right approach depends on whether you're adjusting the overall SVG or individual elements and animations within it.