Paths represent the outline of a shape which can be filled, stroked, (see Filling, Stroking and Paint Servers) used as a clipping path (see Clipping, Masking and Compositing), or for any combination of the three.
A path is described using the concept of a current point. In an analogy with drawing on paper, the current point can be thought of as the location of the pen. The position of the pen can be changed, and the outline of a shape (open or closed) can be traced by dragging the pen in either straight lines or curves.
Paths represent an outline of an object which is defined in terms of moveto (set a new current point), lineto (draw a straight line), curveto (draw a curve using a cubic bezier), arc (elliptical or circular arc) and closepath (close the current shape by drawing a line to the last moveto) elements. Compound paths (i.e., a path with subpaths, each consisting of a single moveto followed by one or more line or curve operations) are possible to allow effects such as "donut holes" in objects.
A path is defined in SVG using the <path> element.
<!ELEMENT path (desc?,title?) > <!ATTLIST path id ID #IMPLIED xml:lang NMTOKEN #IMPLIED xml:space (default|preserve) #IMPLIED class NMTOKENS #IMPLIED style CDATA #IMPLIED transform CDATA #IMPLIED %graphicsElementEvents; system-required CDATA #IMPLIED d CDATA #REQUIRED flatness CDATA #IMPLIED nominalLength CDATA #IMPLIED > |
Attribute definitions:
A path is defined by including a <path> element which contains a d="(path data)" attribute, where the d attribute contains the moveto, line, curve (both cubic and quadratic beziers), arc and closepath instructions. The following example specifies a path in the shape of a triangle. (The M indicates a moveto, the L's indicate lineto's, and the z indicates a closepath:
<?xml version="1.0" standalone="yes"?> <svg width="4in" height="3in" xmlns = 'http://www.w3.org/Graphics/SVG/svg-19990730.dtd'> <path d="M 100 100 L 140 100 L 120 140 z"/> </svg>
Path data values can contain newline characters and thus can be broken up into multiple lines to improve readability. Because of line length limitations with certain related tools, it is recommended that SVG generators split long path data strings across multiple lines, with each line not exceeding 255 characters. Also note that newline characters are only allowed at certain places within a path data value.
The syntax of path data is very abbreviated in order to allow for minimal file size and efficient downloads, since many SVG files will be dominated by their path data. Some of the ways that SVG attempts to minimize the size of path data are as follows:
The path data syntax is a prefix notation (i.e., commands followed by parameters). The only allowable decimal point is a period (".") and no other delimiter characters are allowed. (For example, the following is an invalid numeric value in a path data stream: "13,000.56". Instead, you should say: "13000.56".)
(??? Need to clean this up) In the tables below, the following notation is used:
The following sections list the commands.
The "moveto" commands (M or m) establish a new current point. The effect is as if the "pen" were lifted and moved to a new location. A path data segment must begin with either one of the "moveto" commands or one of the "arc" commands. Subsequent "moveto" commands (i.e., when the "moveto" is not the first command) represent the start of a new subpath:
Command | Name | Parameters | Description |
---|---|---|---|
M (absolute) m (relative) |
moveto | (x y)+ | Start a new sub-path at the given (x,y) coordinate. M (uppercase) indicates that absolute coordinates will follow; m (lowercase) indicates that relative coordinates will follow. If a relative moveto (m) appears as the first element of the path, then it is treated as a pair of absolute coordinates. If a moveto is followed by multiple pairs of coordinates, the subsequent pairs are treated as implicit lineto commands. |
The "closepath" (Z or z) causes an automatic straight line to be drawn from the current point to the initial point of the current subpath. "Closepath" differs in behavior from what happens when "manually" closing a subpath via a "lineto" command in how 'stroke-linejoin' and 'stroke-linecap' are implemented. With "closepath", the end of the final segment of the subpath is "joined" with the start of the initial segment of the subpath using the current value of 'stroke-linejoin' . If you instead "manually" close the subpath via a "lineto" command, the start of the first segment and the end of the last segment are not joined but instead are each capped using the current value of 'stroke-linecap':
Command | Name | Parameters | Description |
---|---|---|---|
Z or z |
closepath | (none) | Close the current subpath by drawing a straight line from the current point to current subpath's most recent starting point (usually, the most recent moveto point). |
The various "lineto" commands draw straight lines from the current point to a new point:
Command | Name | Parameters | Description |
---|---|---|---|
L (absolute) l (relative) |
lineto | (x y)+ | Draw a line from the current point to the given (x,y) coordinate which becomes the new current point. L (uppercase) indicates that absolute coordinates will follow; l (lowercase) indicates that relative coordinates will follow. A number of coordinates pairs may be specified to draw a polyline. At the end of the command, the new current point is set to the final set of coordinates provided. |
H (absolute) h (relative) |
horizontal lineto | x+ | Draws a horizontal line from the current point (cpx, cpy) to (x, cpy). H (uppercase) indicates that absolute coordinates will follow; h (lowercase) indicates that relative coordinates will follow. Multiple x values can be provided (although usually this doesn't make sense). At the end of the command, the new current point becomes (x, cpy) for the final value of x. |
V (absolute) v (relative) |
vertical lineto | y+ | Draws a vertical line from the current point (cpx, cpy) to (cpx, y). V (uppercase) indicates that absolute coordinates will follow; v (lowercase) indicates that relative coordinates will follow. Multiple y values can be provided (although usually this doesn't make sense). At the end of the command, the new current point becomes (cpx, y) for the final value of y. |
These three groups of commands that draw curves:
x = cx + rx * cos(theta) y = cy + ry * sin(theta)where the elliptical arc is drawn as a sweep for every possible theta between a given start angle and end engle.
The cubic bezier commands are as follows:
Command | Name | Parameters | Description |
---|---|---|---|
C (absolute) c (relative) |
curveto | (x1 y1 x2 y2 x y)+ | Draws a cubic bezier curve from the current point to (x,y) using (x1,y1) as the control point at the beginning of the curve and (x2,y2) as the control point at the end of the curve. C (uppercase) indicates that absolute coordinates will follow; c (lowercase) indicates that relative coordinates will follow. Multiple sets of coordinates may be specified to draw a polybezier. At the end of the command, the new current point becomes the final (x,y) coordinate pair used in the polybezier. |
S (absolute) s (relative) |
shorthand/smooth curveto | (x2 y2 x y)+ | Draws a cubic bezier curve from the current point to (x,y). The first control point is assumed to be the reflection of the second control point on the previous command relative to the current point. (If there is no previous command or if the previous command was not an C, c, S or s, assume the first control point is coincident with the current point.) (x2,y2) is the second control point (i.e., the control point at the end of the curve). S (uppercase) indicates that absolute coordinates will follow; s (lowercase) indicates that relative coordinates will follow. Multiple sets of coordinates may be specified to draw a polybezier. At the end of the command, the new current point becomes the final (x,y) coordinate pair used in the polybezier. |
The quadratic bezier commands are as follows:
Command | Name | Parameters | Description |
---|---|---|---|
Q (absolute) q (relative) |
quadratic bezier curveto | (x1 y1 x y)+ | Draws a quadratic bezier curve from the current point to (x,y) using (x1,y1) as the control point. Q (uppercase) indicates that absolute coordinates will follow; q (lowercase) indicates that relative coordinates will follow. Multiple sets of coordinates may be specified to draw a polybezier. At the end of the command, the new current point becomes the final (x,y) coordinate pair used in the polybezier. |
T (absolute) t (relative) |
Shorthand/smooth quadratic bezier curveto | (x y)+ | Draws a quadratic bezier curve from the current point to (x,y). The control point is assumed to be the reflection of the control point on the previous command relative to the current point. (If there is no previous command or if the previous command was not an Q, q, T or t, assume the control point is coincident with the current point.) T (uppercase) indicates that absolute coordinates will follow; t (lowercase) indicates that relative coordinates will follow. At the end of the command, the new current point becomes the final (x,y) coordinate pair used in the polybezier. |
The elliptical arc commands are as follows:
Command | Name | Parameters | Description |
---|---|---|---|
A (absolute) a (relative) |
elliptical arc | (rx ry x-axis-rotation large-arc-flag sweep-flag x y)+ | Draws an elliptical arc from the current point to (x, y). The size and orientation of the ellipse is defined two radii (rx, ry) and an x-axis-rotation, which indicates how the ellipse as a whole is rotated relative to the current coordinate system. The center (cx, cy) of the ellipse is calculated automatically to satisfy the constraints imposed by the other parameters. large-arc-flag and sweep-flag contribute to the automatic calculations and help determine how the arc is drawn. |
The elliptical arc command draws a section of an ellipse which meets the following constraints:
(We need examples to illustrate all of this! Here is one for the moment.
Suppose you have a circle with center (5,5) and radius 2 and you wish to
draw an arc from 0 degrees to 90 degrees. Then one way to achieve this would
be M 7,5 A 2,2 0 0 1 5,7
. In this example, you move to the
"0 degree" location on the circle, which is (7,5), since the center is at (5,5)
and the circle has radius 2. Since we have circle, the two radii are the same, and in
this example both are equal to 2. Since our sweep is 90 degrees, which is less than 180,
we set large-arc-flag to 0. We want to draw the sweep in a positive angle
direction, so we set sweep-flag to 1. Since we want to draw the arc to the point which is
at the 90 degree location of the circle,
we set (x,y) to (5,7).)
(??? This requires clean-up and a more formal write-up on the terminology.) The following is the BNF for SVG paths. The following notation is used:
svg-path: wsp* subpaths? subpaths: subpath | subpath subpaths subpath: moveto subpath-elements? subpath-elements: subpath-element-wsp | subpath-element-wsp subpath-elements subpath-element-wsp: subpath-element wsp* subpath-element: closepath | lineto | horizontal-lineto | vertical-lineto | curveto | smooth-curveto | quadratic-bezier-curveto | smooth-quadratic-bezier-curveto | elliptical-arc moveto: ( "M" | "m" ) wsp* moveto-argument-sequence moveto-argument-sequence: coordinate-pair | coordinate-pair lineto-argument-sequence closepath: ("Z" | "z") wsp* lineto: ( "L" | "l" ) wsp* lineto-argument-sequence lineto-argument-sequence: coordinate-pair | coordinate-pair lineto-argument-sequence horizontal-lineto: ( "H" | "h" ) wsp* horizontal-lineto-argument-sequence horizontal-lineto-argument-sequence: horizontal-lineto-argument | horizontal-lineto-argument horizontal-lineto-argument-sequence horizontal-lineto-argument: coordinate vertical-lineto: ( "V" | "v" ) wsp* vertical-lineto-argument-sequence vertical-lineto-argument-sequence: vertical-lineto-argument | vertical-lineto-argument vertical-lineto-argument-sequence vertical-lineto-argument: coordinate curveto: ( "C" | "c" ) wsp* curveto-argument-sequence curveto-argument-sequence: curveto-argument | curveto-argument curveto-argument-sequence curveto-argument: coordinate-pair coordinate-pair coordinate-pair smooth-curveto: ( "S" | "s" ) wsp* smooth-curveto-argument-sequence smooth-curveto-argument-sequence: smooth-curveto-argument | smooth-curveto-argument smooth-curveto-argument-sequence smooth-curveto-argument: coordinate-pair coordinate-pair quadratic-bezier-curveto: ( "Q" | "q" ) wsp* quadratic-bezier-curveto-argument-sequence quadratic-bezier-curveto-argument-sequence: quadratic-bezier-curveto-argument | quadratic-bezier-curveto-argument quadratic-bezier-curveto-argument-sequence quadratic-bezier-curveto-argument: coordinate-pair coordinate-pair smooth-quadratic-bezier-curveto: ( "T" | "t" ) wsp* smooth-quadratic-bezier-curveto-argument-sequence smooth-quadratic-bezier-curveto-argument-sequence: coordinate-pair | coordinate-pair smooth-quadratic-bezier-curveto-argument-sequence elliptical-arc: ( "A" | "a" ) wsp* elliptical-arc-argument-sequence elliptical-arc-argument-sequence: elliptical-arc-argument | elliptical-arc-argument elliptical-arc-argument-sequence elliptical-arc-argument: nonnegative-number-comma-wsp nonnegative-number-comma-wsp number-comma-wsp flag-comma-wsp flag-comma-wsp coordinate-pair coordinate-pair: coordinate coordinate coordinate: number-comma-wsp nonnegative-number-comma-wsp: nonnegative-number wsp* comma? wsp* number-comma-wsp: number wsp* comma? wsp* nonnegative-number: integer-constant | floating-point-constant number: sign? integer-constant | sign? floating-point-constant flag-comma-wsp: flag wsp* comma? wsp* flag: "0" | "1" comma: "," integer-constant: digit-sequence floating-point-constant: fractional-constant exponent? | digit-sequence exponent fractional-constant: digit-sequence? "." digit-sequence | digit-sequence "." exponent: ( "e" | "E" ) sign? digit-sequence sign: "+" | "-" digit-sequence: digit | digit digit-sequence digit: "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9" wsp: (#x20 | #x9 | #xD | #xA)+