shiny/iconvg: link to the canonical spec
Change-Id: Ib006cf872d79acf785fa5bffde9b8e32bcf5439b
Reviewed-on: https://go-review.googlesource.com/c/exp/+/323550
Reviewed-by: Rob Pike <r@golang.org>
Trust: Nigel Tao <nigeltao@golang.org>
diff --git a/shiny/iconvg/doc.go b/shiny/iconvg/doc.go
index a16871a..559b040 100644
--- a/shiny/iconvg/doc.go
+++ b/shiny/iconvg/doc.go
@@ -8,656 +8,14 @@
WARNING: THIS FORMAT IS EXPERIMENTAL AND SUBJECT TO INCOMPATIBLE CHANGES.
-It is similar in concept to SVG (Scalable Vector Graphics) but much simpler.
-Compared to "SVG Tiny", it does not have features for text, multimedia,
-interactivity, linking, scripting, animation, XSLT, DOM, combination with
-raster graphics such as JPEG formatted textures, etc.
+A longer overview is at
+https://github.com/google/iconvg
-It is a format for efficient presentation, not an authoring format. For
-example, it does not provide grouping individual paths into higher level
-objects. Instead, the anticipated workflow is that artists use other tools and
-authoring formats like Inkscape and SVG, or commercial equivalents, and export
-IconVG versions of their assets, the same way that they would produce PNG
-versions of their vector art. It is not a goal to be able to recover the
-original SVG from a derived IconVG.
+The file format is specified at
+https://github.com/google/iconvg/blob/main/spec/iconvg-spec.md
-It is not a pixel-exact format. Different implementations may produce slightly
-different renderings, due to implementation-specific rounding errors in the
-mathematical computations when rasterizing vector paths to pixels. Artifacts
-may appear when scaling up to extreme sizes, say 1 million by 1 million pixels.
-Nonetheless, at typical scales, e.g. up to 4096 × 4096, such differences are
-not expected to be perceptible to the naked eye.
-
-The encoder aims to emit byte-identical output for the same input, independent
-of the platform (and specifically its floating-point hardware).
-
-
-Structure
-
-An IconVG graphic consists of a magic identifier, one or more metadata bytes
-then a sequence of variable length instructions for a virtual machine.
-
-Those instructions encode a sequence of filled paths, similar to SVG path data
-(https://www.w3.org/TR/SVG/paths.html#PathData). Rendering involves switching
-between two modes: a styling mode where color registers are set, and a drawing
-mode where a path's geometry is defined. The virtual machine starts in the
-styling mode.
-
-In both modes, rendering proceeds by reading a one byte opcode followed by a
-variable number of data bytes for that opcode. The mapping from byte values to
-opcodes depends on whether the renderer is in the styling or drawing mode. A
-0x07 byte value means setting the color selector register in the styling mode,
-and means adding multiple lineto segments in the drawing mode.
-
-
-Level of Detail
-
-The machine state includes 2 level of detail registers, denoted LOD0 and LOD1,
-both float32 values, initialized to +0 and +infinity. Drawing mode opcodes have
-no effect (other than leaving drawing mode) unless the height H in pixels of
-the rasterization satisfies LOD0 <= H and H < LOD1.
-
-This allows the format to provide a simpler version for small rasterizations
-(e.g. below 32 pixels) and a more complex version for large rasterizations
-(e.g. 32 and above pixels).
-
-
-Registers
-
-The machine state includes 64 color registers (denoted CREG[0], CREG[1], ...,
-CREG[63]) and 64 number registers (denoted NREG[0], NREG[1], ..., NREG[63]).
-Register indexing is done modulo 64, so CREG[70] is the same as CREG[6], and
-CREG[-1] is the same as CREG[63].
-
-Each CREG and NREG register is 32 bits wide. The CREG registers are initialized
-to the custom palette (see below); the NREG registers are initialized to 0. The
-machine state also includes two selector registers, denoted CSEL and NSEL. They
-are effectively 6 bit integers, as they index CREG and NREG, and are also
-initialized to 0.
-
-Color registers are four uint8 values: red, green, blue and alpha.
-
-Number registers are float32 values.
-
-
-Colors and Gradients
-
-IconVG graphics work in 32 bit alpha-premultiplied color, with 8 bits for red,
-green, blue and alpha. Alpha-premultiplication means that c00000c0 represents a
-75%-opaque, fully saturated red.
-
-It also means that some RGBA combinations (where e.g. the red value is greater
-than the alpha value) are nonsensical. The virtual machine re-purposes some of
-those values to represent gradients instead of flat colors. Any color register
-whose alpha value is zero but whose blue value is at least 128 is a gradient.
-Its remaining bits are reinterpreted such that:
-
-The low 6 bits of the red value is the number of color/offset stops, NSTOPS.
-
-The high 2 bits of the red value are reserved.
-
-The low 6 bits of the green value is the color register base, CBASE.
-
-The high 2 bits of the green value is how to spread the gradient past its
-nominal bounds (from offset being 0.0 to offset being 1.0). The high two bits
-being 0, 1, 2 or 3 mean none, pad, reflect and repeat respectively. None means
-that offsets outside of the [0.0, 1.0] range map to transparent black. Pad
-means that offsets below 0.0 and above 1.0 map to the colors that 0.0 and 1.0
-would map to. Reflect means that the offset mapping is reflected start-to-end,
-end-to-start, start-to-end, etc. Repeat means that the offset mapping is
-repeated start-to-end, start-to-end, start-to-end, etc.
-
-The low 6 bits of the blue value is the number register base, NBASE.
-
-The remaining bit (the 0x40 bit) of the blue value denotes the gradient shape:
-0 means a linear gradient and 1 means a radial gradient.
-
-The gradient has NSTOPS color/offset stops. The first stop has color
-CREG[CBASE+0] and offset NREG[NBASE+0], the second stop has color CREG[CBASE+1]
-and offset NREG[NBASE+1], and so on.
-
-The gradient also uses the six numbers from NREG[NBASE-6] to NREG[NBASE-1],
-which form an affine transformation matrix [a, b, c; d, e, f] such that
-a=NREG[NBASE-6], b=NREG[NBASE-5], c=NREG[NBASE-4], etc. This matrix maps from
-graphic coordinate space (defined by the metadata's viewBox) to gradient
-coordinate space. Gradient coordinate space is where a linear gradient ranges
-from x=0 to x=1, and a radial gradient has center (0, 0) and radius 1.
-
-The graphic coordinate (px, py) maps to the gradient coordinate (dx, dy) by:
-
- dx = a*px + b*py + c
- dy = d*px + e*py + f
-
-The appendix below gives explicit formulae for the [a, b, c; d, e, f] affine
-transformation matrix for common gradient geometry, such as a linear gradient
-defined by two points.
-
-At the time a gradient is used to fill a path, it is invalid for any of the
-stop colors to be out of alpha-premultiplied range (where red, green or blue is
-greater than alpha), including referencing another gradient. It is also invalid
-for any stop offset to be less than or equal to a previous offset, or outside
-the range [0, 1].
-
-
-Colors
-
-Color register values are always 32 bits, or 4 bytes. Colors in the instruction
-byte stream can be encoded more compactly, and are encoded in either 1, 2, 3 or
-4 bytes, depending on context. For example, some opcodes are followed by a 1
-byte color, others by a 2 byte color. There are two forms of 3 byte colors:
-direct and indirect.
-
-For a 1 byte encoding, byte values in the range [0, 125) encode the RGBA color
-where the red, green and blue values come from the base-5 encoding of that byte
-value such that 0, 1, 2, 3 and 4 map to 0x00, 0x40, 0x80, 0xc0, 0xff. The alpha
-value is 0xff. For example, the color 40ffc0ff can be encoded as 0x30, as
-decimal 48 equals 1*25 + 4*5 + 3. A byte value of 125, 126 or 127 mean the
-colors c0c0c0c0, 80808080 and 00000000 respectively. Byte values in the range
-[128, 192) mean a color from the custom palette (indexed by that byte value
-minus 128). Byte values in the range [192, 256) mean the value of a CREG color
-register (with CREG indexed by that byte value minus 192).
-
-For a 2 byte encoding, the red, green, blue and alpha values are all 4 bit
-values. For example, the color 338800ff can be encoded as 0x38 0x0f.
-
-For a 3 byte direct encoding, the red, green and blue values are all 8 bit
-values. The alpha value is implicitly 255. For example, the color 306607ff can
-be encoded as 0x30 0x66 0x07.
-
-For a 4 byte encoding, the red, green, blue and alpha values are all 8 bit
-values. For example, the color 30660780 is simply 0x30 0x66 0x07 0x80.
-
-For a 3 byte indirect encoding, the first byte is an integer value in the range
-[0, 255] (denoted T) and the second and third bytes are each a 1 byte encoded
-color (denoted C0 and C1). The resultant color's red channel value is given by:
- RESULTANT.RED = (((255-T) * C0.RED) + (T * C1.RED) + 128) / 255
-rounded down to an integer value (the mathematical floor function), and
-likewise for the green, blue and alpha channels. For example, if the custom
-palette's third entry is a fully opaque orange, then 0x40 0x7f 0x82 encodes a
-25% percent opaque orange: a blend of 75% times fully transparent (1 byte color
-0x7f) and 25% times a fully opaque orange (1 byte color 0x82).
-
-It is valid for some encodings to yield a color value where the red, green or
-blue value is greater than the alpha value, as this may be a gradient. If it
-isn't a valid gradient, it is equivalent to transparent black and drawing with
-that color is a no-op.
-
-
-Palettes
-
-Rendering an IconVG graphic can be varied by a 64 color palette. For example,
-an emoji graphic may be rendered with palette color 0 for skin and palette
-color 1 for hair. Decorative variations, such as different clothing, can be
-implemented by palette colors possibly set to completely transparent to switch
-paths off.
-
-Rendering software should allow users to pass an optional 64 color palette. If
-one isn't provided, the suggested palette (either given in the metadata or the
-default consisting entirely of opaque black) should be used. Whichever palette
-ends up being used is designated the custom palette.
-
-Some user-given colors may be nonsensical as alpha-premultiplied colors, where
-e.g. the red value is greater than the alpha value. Such colors are replaced by
-opaque black and not re-interpreted as gradients.
-
-Assigning names such as "skin", "hair" or "bow_tie" to the integer indexes of
-that 64 color palette is out of scope of the IconVG format per se.
-
-
-Numbers
-
-Like colors, numbers are encoded in the instruction stream in either 1, 2 or 4
-bytes. Unlike colors, the encoding length is not determined by context.
-Instead, the low two bits of the first byte indicate the encoding length.
-
-If the least significant bit (the 0x01 bit) of the first byte is 0, the number
-is encoded in 1 byte. Otherwise, it is encoded in 2 or 4 bytes depending on the
-second least significant bit (the 0x02 bit) of the first byte being 0 or 1.
-
-
-Natural Numbers
-
-For a 1 byte encoding, the remaining 7 bits form an integer value in the range
-[0, 1<<7). For example, 0x28 encodes the value 0x14 or, in decimal, 20.
-
-For a 2 byte encoding, the remaining 14 bits, interpreted as little endian,
-form an integer in the range [0, 1<<14). For example, 0x59 0x83 encodes the
-value 0x20d6 or, in decimal, 8406.
-
-For a 4 byte encoding, the remaining 30 bits, interpreted as little endian,
-form an integer in the range [0, 1<<30). For example, 0x07 0x00 0x80 0x3f
-encodes the value 0xfe00001 or, in decimal, 266338305.
-
-
-Real Numbers
-
-The encoding of a real number resembles the encoding of a natural number. For 1
-and 2 byte encodings, the decoded real number equals the decoded natural
-number. For example, 0x28 encodes the real number 20.0, just as it encodes the
-natural number 20.
-
-For a 4 byte encoding, the decoded natural number, in the range [0, 1<<30), is
-shifted left by 2, to make a uint32 value that is a multiple of 4. The decoded
-real number is the floating point number corresponding to the IEEE 754 binary
-representation of that uint32 (i.e. a reinterpretation as a float32). For
-example, 0x07 0x00 0x80 0x3f encodes the value 1.000000476837158203125.
-
-It is valid for the 4 byte encoding to represent infinities and NaNs, but if
-not loaded into LOD0 or LOD1, the subsequent rendering is undefined.
-
-
-Coordinate Numbers
-
-The encoding of a coordinate number resembles the encoding of a real number.
-For 1 and 2 byte encodings, the decoded coordinate number equals (R*scale -
-bias), where R is the decoded real number as above. The scale and bias depends
-on the number of bytes in the encoding.
-
-For a 1 byte encoding, the scale is 1 and the bias is 64, so that a 1 byte
-coordinate ranges in [-64, +64) at integer granularity. For example, the
-coordinate 7 can be encoded as 0x8e.
-
-For a 2 byte encoding, the scale is 1/64 and the bias is 128, so that a 2 byte
-coordinate ranges in [-128, +128) at 1/64 granularity. For example, the
-coordinate 7.5 can be encoded as 0x81 0x87.
-
-For a 4 byte encoding, the decoded coordinate number simply equals R. For
-example, the coordinate 7.5 can also be encoded as 0x03 0x00 0xf0 0x40.
-
-
-Zero-to-One Numbers
-
-A zero-to-one number is a real number that is typically in the range [0, 1],
-although it is valid for a value to be outside of that range. For example,
-angles are expressed as a zero-to-one number: a fraction of a complete
-revolution (360 degrees). Gradient stop offsets are another example.
-
-The encoding of a zero-to-one number resembles the encoding of a real number.
-For 1 and 2 byte encodings, the decoded number equals R*scale, where R is the
-decoded real number as above. The scale depends on the number of bytes in the
-encoding.
-
-For a 1 byte encoding, the real number (ranging up to 128) is scaled by 1/120.
-The denominator is 2*2*2 * 3 * 5, so that 15 degrees (2*π/24 radians) can be
-encoded as 0x0a.
-
-For a 2 byte encoding, the real number (ranging up to 16384) is scaled by
-1/15120. The denominator is 2*2*2*2 * 3*3*3 * 5 * 7. For example, 40 degrees
-(2*π/9 radians) can be encoded as 0x41 0x1a.
-
-For a 4 byte encoding, the decoded zero-to-one number simply equals R. For
-example, 1 degree (2*π/360 radians), or 0.002777777..., can be approximated by
-the encoding 0x63 0x0b 0x36 0x3b.
-
-
-Magic Identifier
-
-An IconVG graphic starts with the four bytes 0x89 0x49 0x56 0x47 ("\x89IVG").
-
-
-Metadata
-
-The encoded metadata starts with a natural number (see encoding above) of the
-number of metadata chunks in the metadata, followed by that many chunks. Each
-chunk starts with the length remaining in the chunk (again, encoded as a
-natural number), not including the chunk length itself. After that is a MID
-(Metadata Identifier) natural number, then MID-specific data. Chunks must be
-presented in increasing MID order. MIDs cannot be repeated. All MIDs are
-optional.
-
-
-MID 0 - ViewBox
-
-Metadata Identifier 0 means that the MID-specific data contains four coordinate
-values (see above for the coordinate encoding). These are the minX, minY, maxX,
-maxY of the graphic's viewBox: its bounding rectangle in (scalable) vector
-space. Note that these are abstract units, and not necessarily 1:1 with pixels.
-If this MID is not present, the viewBox defaults to (-32, -32, +32, +32). A
-viewBox is invalid if minX > maxX or if minY > maxY or if at least one of those
-four values are a NaN or an infinity.
-
-
-MID 1 - Suggested Palette
-
-Metadata Identifier 1 means that the MID-specific data contains a suggested
-palette, e.g. to provide a default rendering of variable colors such as an
-emoji's skin and hair. The suggested palette is encoded in at least one byte.
-The low 6 bits of that byte form a number N. The high 2 bits denote the palette
-color format: those high 2 bits being 0, 1, 2 or 3 mean 1, 2, 3 (direct) or 4
-byte colors (see above for the color encoding). The chunk then contains N+1
-explicit colors, in that 1, 2, 3 or 4 byte encoding. A palette has exactly 64
-colors, the 63-N implicit colors of the suggested palette are set to opaque
-black. A 1 byte color that refers to the custom palette or a CREG color
-register resolves to opaque black. If this MID is not present, the suggested
-palette consists entirely of opaque black, as black is always fashionable.
-
-
-Styling Opcodes
-
-Some opcode descriptions refer to an adjustment value, ADJ. That value is the
-low three bits of the opcode, nominally in the range [0, 8), although in
-practice the range is [0, 7) as no ADJ-using opcode has the low three bits set.
-
-Opcodes 0x00 to 0x3f sets CSEL to the low 6 bits of the opcode.
-
-Opcodes 0x40 to 0x7f sets NSEL to the low 6 bits of the opcode.
-
-Opcodes 0x80 to 0x86 sets CREG[CSEL-ADJ] to the 1 byte encoded color following
-the opcode.
-
-Opcodes 0x88 to 0x8e sets CREG[CSEL-ADJ] to the 2 byte encoded color following
-the opcode.
-
-Opcodes 0x90 to 0x96 sets CREG[CSEL-ADJ] to the 3 byte direct encoded color
-following the opcode.
-
-Opcodes 0x98 to 0x9e sets CREG[CSEL-ADJ] to the 4 byte encoded color following
-the opcode.
-
-Opcodes 0xa0 to 0xa6 sets CREG[CSEL-ADJ] to the 3 byte indirect encoded color
-following the opcode.
-
-Opcodes 0x87, 0x8f, 0x97, 0x9f and 0xa7 sets CREG[CSEL] to the 1, 2, 3
-(direct), 4 and 3 (indirect) byte encoded color, following the opcode, and then
-increments CSEL by 1.
-
-Opcodes 0xa8 to 0xae sets NREG[NSEL-ADJ] to the real number following the
-opcode.
-
-Opcodes 0xb0 to 0xb6 sets NREG[NSEL-ADJ] to the coordinate number following the
-opcode.
-
-Opcodes 0xb8 to 0xbe sets NREG[NSEL-ADJ] to the zero-to-one number following
-the opcode.
-
-Opcode 0xaf, 0xb7 and 0xbf sets NREG[NSEL] to the real, coordinate and
-zero-to-one number following the opcode, and then increments NSEL by 1.
-
-Opcodes 0xc0 to 0xc6 switches to the drawing mode, and is followed by two
-coordinates that is the path's starting location. In effect, there is an
-implicit M (absolute moveto) op. CREG[CSEL-ADJ], either a flat color or a
-gradient, will fill the path once it is complete.
-
-Opcode 0xc7 sets the Level of Detail bounds LOD0 and LOD1 to the two real
-numbers following the opcode.
-
-All other opcodes are reserved.
-
-
-Drawing Opcodes
-
-The drawing model is based on SVG path data
-(https://www.w3.org/TR/SVG/paths.html#PathData) and this description re-uses
-SVG's one-letter mnemonics: M means absolute moveto, m means relative moveto, L
-means absolute lineto, l means relative lineto, H means absolute horizontal
-lineto, etc. Upper and lower case mean absolute and relative coordinates. The
-upper case mnemonics of the SVG operations used in IconVG's drawing mode are:
-M, Z, L, H, V, C, S, Q, T, A.
-
-IconVG differs from SVG with multiple consecutive moveto ops. SVG treats all
-but the first one as lineto ops. IconVG treats them all as moveto ops.
-
-Almost all opcodes, i.e. those in the range [0x00, 0xdf], come in contiguous
-groups of 16 or 32. For example, there are 16 Q (absolute quadratic Bézier
-curveto) opcodes, from 0x60 to 0x6f. Those opcodes' meaning differ only in
-their repeat count RC: how often that drawing operation is repeated. The lowest
-valued opcode has a repeat count of 1, the next lowest has a repeat count of 2
-and so on. For example, the opcode 0x68 means 9 consecutive Q drawing ops.
-
-Opcodes 0x00 to 0x1f means RC consecutive L ops, for RC in [1, 32]. The opcode
-is followed by 2*RC coordinates, RC sets of (x, y).
-
-Opcodes 0x20 to 0x3f are like the previous paragraph, except L (absolute)
-becomes l (relative).
-
-Opcodes 0x40 to 0x4f means RC consecutive T ops, for RC in [1, 16]. The opcode
-is followed by 2*RC coordinates, RC sets of (x, y).
-
-Opcodes 0x50 to 0x5f are like the previous paragraph, except T (absolute)
-becomes t (relative).
-
-Opcodes 0x60 to 0x6f means RC consecutive Q ops, for RC in [1, 16]. The opcode
-is followed by 4*RC coordinates, RC sets of (x1, y1, x, y).
-
-Opcodes 0x70 to 0x7f are like the previous paragraph, except Q (absolute)
-becomes q (relative).
-
-Opcodes 0x80 to 0x8f means RC consecutive S ops, for RC in [1, 16]. The opcode
-is followed by 4*RC coordinates, RC sets of (x2, y2, x, y).
-
-Opcodes 0x90 to 0x9f are like the previous paragraph, except S (absolute)
-becomes s (relative).
-
-Opcodes 0xa0 to 0xaf means RC consecutive C ops, for RC in [1, 16]. The opcode
-is followed by 6*RC coordinates, RC sets of (x1, y1, x2, y2, x, y).
-
-Opcodes 0xb0 to 0xbf are like the previous paragraph, except C (absolute)
-becomes c (relative).
-
-Opcodes 0xc0 to 0xcf means RC consecutive A ops, for RC in [1, 16]. The opcode
-is followed by 6*RC numbers, RC sets of (rx, ry, xAxisRotation, flags, x, y).
-The rx, ry, x and y numbers are coordinates. The xAxisRotation number is an
-angle (a zero-to-one number being a fraction of 360 degrees). The flags are
-encoded as a natural number. The 0x01 bit of the decoded natural number is the
-large-arc-flag and the 0x02 bit is the sweep-flag.
-
-Opcodes 0xd0 to 0xdf are like the previous paragraph, except A (absolute)
-becomes a (relative).
-
-Opcode 0xe0 is reserved. (A future version of IconVG may use this opcode to
-mean the same as 0xe1 without the one z op, which will matter for stroked
-paths).
-
-Opcode 0xe1 means one z op and then end the path: fill the path with the color
-chosen when we switched to the drawing mode, and switch back to the styling
-mode. (The Z and z ops are equivalent).
-
-Opcode 0xe2 means one z op and then an implicit M op to the (x, y) coordinates
-after the opcode.
-
-Opcode 0xe3 means one z op and then an implicit m op to the (x, y) coordinates
-after the opcode.
-
-Opcodes 0xe4 and 0xe5 are reserved. (A future version of IconVG may use these
-for M and m ops, if we allow stroked paths).
-
-Opcode 0xe6 means one H op to the x coordinate after the opcode.
-
-Opcode 0xe7 means one h op to the x coordinate after the opcode.
-
-Opcode 0xe8 means one V op to the y coordinate after the opcode.
-
-Opcode 0xe9 means one v op to the y coordinate after the opcode.
-
-All other opcodes are reserved.
-
-These opcode descriptions all assume that the Level of Detail constraint (see
-above) is satisfied. If not, the opcodes and their variable length data are
-consumed, but no further action is taken (other than leaving drawing mode).
-
-
-Example
-
-The production version of the "action/info" icon from the Material Design icon
-set is defined by the following SVG, also available at
-https://github.com/google/material-design-icons/blob/3.0.2/action/svg/production/ic_info_48px.svg:
-
- <svg xmlns="http://www.w3.org/2000/svg" width="48" height="48" viewBox="0 0 48 48">
- <path d="M24 4C12.95 4 4 12.95 4 24s8.95 20 20 20 20-8.95 20-20S35.05 4 24 4z
- m2 30h-4V22h4v12zm0-16h-4v-4h4v4z"/></svg>
-
-This is 202 bytes, or 174 bytes after "gzip --best". The PNG renderings at
-various sizes:
-
- 18x18: 207 bytes
- 24x24: 222 bytes
- 36x36: 321 bytes
- 48x48: 412 bytes
-
-The corresponding IconVG is 73 bytes:
-
- 89 49 56 47 02 0a 00 50 50 b0 b0 c0 80 58 a0 cf
- cc 30 c1 58 58 cf cc 30 c1 58 80 91 37 33 0f 41
- a8 a8 a8 a8 37 33 0f c1 a8 58 80 cf cc 30 41 58
- 80 58 e3 84 bc e7 78 e8 7c e7 88 e9 98 e3 80 60
- e7 78 e9 78 e7 88 e9 88 e1
-
-The annotated version is below. Note that the IconVG viewBox ranges from -24 to
-+24 while the SVG viewBox ranges from 0 to 48.
-
- 89 49 56 47 IconVG Magic identifier
- 02 Number of metadata chunks: 1
- 0a Metadata chunk length: 5
- 00 Metadata Identifier: 0 (viewBox)
- 50 -24
- 50 -24
- b0 +24
- b0 +24
- c0 Start path, filled with CREG[CSEL-0]; M (absolute moveTo)
- 80 +0
- 58 -20
- a0 C (absolute cubeTo), 1 reps
- cf cc 30 c1 -11.049999
- 58 -20
- 58 -20
- cf cc 30 c1 -11.049999
- 58 -20
- 80 +0
- 91 s (relative smooth cubeTo), 2 reps
- 37 33 0f 41 +8.950001
- a8 +20
- a8 +20
- a8 +20
- s (relative smooth cubeTo), implicit
- a8 +20
- 37 33 0f c1 -8.950001
- a8 +20
- 58 -20
- 80 S (absolute smooth cubeTo), 1 reps
- cf cc 30 41 +11.049999
- 58 -20
- 80 +0
- 58 -20
- e3 z (closePath); m (relative moveTo)
- 84 +2
- bc +30
- e7 h (relative horizontal lineTo)
- 78 -4
- e8 V (absolute vertical lineTo)
- 7c -2
- e7 h (relative horizontal lineTo)
- 88 +4
- e9 v (relative vertical lineTo)
- 98 +12
- e3 z (closePath); m (relative moveTo)
- 80 +0
- 60 -16
- e7 h (relative horizontal lineTo)
- 78 -4
- e9 v (relative vertical lineTo)
- 78 -4
- e7 h (relative horizontal lineTo)
- 88 +4
- e9 v (relative vertical lineTo)
- 88 +4
- e1 z (closePath); end path
-
-There are more examples in the ./testdata directory.
-
-
-Appendix - Gradient Transformation Matrices
-
-This appendix derives the affine transformation matrices [a, b, c; d, e, f] for
-linear, circular and elliptical gradients.
-
-
-Linear Gradients
-
-For a linear gradient from (x1, y1) to (x2, y2), let dx, dy = x2-x1, y2-y1. In
-gradient coordinate space, the y-coordinate is ignored, so the transformation
-matrix simplifies to [a, b, c; 0, 0, 0]. It satisfies the three simultaneous
-equations:
-
- a*(x1 ) + b*(y1 ) + c = 0 (eq L.0)
- a*(x1+dy) + b*(y1-dx) + c = 0 (eq L.1)
- a*(x1+dx) + b*(y1+dy) + c = 1 (eq L.2)
-
-Subtracting equation L.0 from equations L.1 and L.2 yields:
-
- a*dy - b*dx = 0
- a*dx + b*dy = 1
-
-So that
-
- a*dy*dy - b*dx*dy = 0
- a*dx*dx + b*dx*dy = dx
-
-Overall:
-
- a = dx / (dx*dx + dy*dy)
- b = dy / (dx*dx + dy*dy)
- c = -a*x1 - b*y1
- d = 0
- e = 0
- f = 0
-
-
-Circular Gradients
-
-For a circular gradient with center (cx, cy) and radius vector (rx, ry), such
-that (cx+rx, cy+ry) is on the circle, let
-
- r = math.Sqrt(rx*rx + ry*ry)
-
-The transformation matrix maps (cx, cy) to (0, 0), maps (cx+r, cy) to (1, 0)
-and maps (cx, cy+r) to (0, 1). Solving those six simultaneous equations give:
-
- a = +1 / r
- b = +0 / r
- c = -cx / r
- d = +0 / r
- e = +1 / r
- f = -cy / r
-
-
-Elliptical Gradients
-
-For an elliptical gradient with center (cx, cy) and axis vectors (rx, ry) and
-(sx, sy), such that (cx+rx, cx+ry) and (cx+sx, cx+sy) are on the ellipse, the
-transformation matrix satisfies the six simultaneous equations:
-
- a*(cx ) + b*(cy ) + c = 0 (eq E.0)
- a*(cx+rx) + b*(cy+ry) + c = 1 (eq E.1)
- a*(cx+sx) + b*(cy+sy) + c = 0 (eq E.2)
- d*(cx ) + e*(cy ) + f = 0 (eq E.3)
- d*(cx+rx) + e*(cy+ry) + f = 0 (eq E.4)
- d*(cx+sx) + e*(cy+sy) + f = 1 (eq E.5)
-
-Subtracting equation E.0 from equations E.1 and E.2 yields:
-
- a*rx + b*ry = 1
- a*sx + b*sy = 0
-
-Solving these two simultaneous equations yields:
-
- a = +sy / (rx*sy - sx*ry)
- b = -sx / (rx*sy - sx*ry)
-
-Re-arranging E.0 yields:
-
- c = -a*cx - b*cy
-
-Similarly for d, e and f so that, overall:
-
- a = +sy / (rx*sy - sx*ry)
- b = -sx / (rx*sy - sx*ry)
- c = -a*cx - b*cy
- d = -ry / (rx*sy - sx*ry)
- e = +rx / (rx*sy - sx*ry)
- f = -d*cx - e*cy
-
-Note that if rx = r, ry = 0, sx = 0 and sy = r then this simplifies to the
-circular gradient transformation matrix formula, above.
+This package's encoder emits byte-identical output for the same input,
+independent of the platform (and specifically its floating-point hardware).
*/
package iconvg
