Rasterizing polygons into images

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RNavega
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Posts: 355
Joined: Sun Aug 16, 2020 1:28 pm

Rasterizing polygons into images

Post by RNavega »

This is an example script of rasterizing a polygon into a grayscale image (R8 format).
So, starting from SVG data, you generate an Image object from it then draw that Image as needed. Depending on the shape and its size, it's a bit lighter to have it described as SVG data than as a PNG file in your game assets.

Github link:
https://github.com/RNavega/RasterPolygon-Love
Preview.png
Preview.png (14.97 KiB) Viewed 4119 times


A .love file is attached, but if you just want to read the code then here's the main.lua:

Code: Select all

-- ==========================================================
-- Example of rasterizing a simple polyline polygon.
-- By Rafael Navega (2024)
--
-- License: Public Domain
-- ==========================================================

io.stdout:setvbuf('no')


local ffi = require('ffi')

local UINT8_PTR_TYPEOF = ffi.typeof('uint8_t*')
local FLOAT_PTR_TYPEOF = ffi.typeof('float*')
local SIZEOF_FLOAT     = ffi.sizeof('float')


local polygonImage1
local polygonImage2
local r8Shader


-- Returns a LÖVE ByteData object, as well as its uint8_t FFI pointer.
-- The pointer is for modifying the contents.
-- Use makeFloatData() when you need it for a GLSL uniform.
local function makeByteData(totalBytes)
    local data = love.data.newByteData(totalBytes)
    return data, UINT8_PTR_TYPEOF(data:getFFIPointer())
end

-- For use with GLSL uniforms. Unused in this demo.
local function makeFloatData(totalFloats)
    local data = love.data.newByteData(totalFloats * SIZEOF_FLOAT)
    return data, FLOAT_PTR_TYPEOF(data:getFFIPointer())
end


local function svgPolygonPointsString()
    -- From the Inkscape XML editor (Ctrl + Shift + X), copy-pasting
    -- the text from the "d" attribute (the SVG draw commands).
    return [[
        M 0,0
        V 32
        H 32
        V 0
        Z
        M 2,2
        H 30
        V 30
        H 2
        Z
        M 9.49,3 9.11,3.03 8.76,3.21 4.06,6.89 3.8,7.2 3.69,7.56 3.71,7.94
        3.89,8.29 10.66,16.91
        l -2.35,1.85 -0.16,0.22 -0.01,0.26 0.12,0.23 0.24,0.13 10.47,2.46
        h 0.36
        l 0.31,-0.15 0.22,-0.27 0.08,-0.35 0.1,-10.76 -0.08,-0.26 -0.19,-0.17
        -0.25,-0.05 -0.25,0.1 -2.35,1.84
        L 10.16,3.37 9.86,3.12
        Z
        M 20.5,24 17.58,24.2 15.2,24.73 13.59,25.53 13,26.5
        l 0.59,0.97 1.61,0.79 2.38,0.54
        L 20.5,29 23.42,28.8 25.8,28.27 27.41,27.47 28,26.5 27.41,25.53
        25.8,24.73 23.42,24.2
        Z
    ]]
end


-- Pixel shader to draw an image in the format "r8" (only a red channel).
-- This is needed because if no shader is used, the result is tinted red.
local R8_PIXEL_SOURCE = [[
vec4 effect( vec4 color, Image tex, vec2 texture_coords, vec2 screen_coords )
{
    float alpha = Texel(tex, texture_coords).r;
    const vec4 HALF_GREY = vec4(vec3(0.5), 1.0);
    return mix(HALF_GREY, vec4(color.xyz, 1.0), alpha);
}
]]


-- Parses the SVG "d" attribute draw command list.
-- Only linear drawings are supported (M/m, L/l, H/h and V/v).
-- Curve, arc (C/c, S/s, A/a) etc commands would need to be flattened to lines
-- to be supported.
local function parseSVGDrawCommands(commandString)
    local tableInsert = table.insert

    local state, lowerState
    local shapeData = {shapes={}}
    local currentShape = {}
    local length = 0
    local position = {0.0, 0.0}

    -- Split the "d" string by whitespace, go through each non-whitespace piece.
    for piece in commandString:gmatch('%s*([^%s]+)%s*') do
        lowerPiece = piece:lower()
        if (lowerPiece == 'm' or lowerPiece == 'l'
            or lowerPiece == 'h' or lowerPiece == 'v') then
            state      = piece
            lowerState = lowerPiece
        elseif lowerPiece == 'z' then
            currentShape.length = length
            tableInsert(shapeData.shapes, currentShape)
            currentShape = {}
            length = 0
        else
            -- Try to read a single number ("135.002"), or a comma-separated
            -- pair of numbers ("135.002,-99.71"), with the numbers possibly
            -- having decimal points and/or preceded by a negative sign.
            local valueA, valueB = piece:match('([%-%d%.]+)[,]*([%-%d%.]*)')
            if valueA then
                valueA = tonumber(valueA)
                if lowerState == 'l' or lowerState == 'm' then
                    if valueB then
                        valueB = tonumber(valueB)
                        if state == 'M' or state == 'L' then
                            position[1] = valueA
                            position[2] = valueB
                        else
                            position[1] = position[1] + valueA
                            position[2] = position[2] + valueB
                        end
                        currentShape[length + 1] = position[1]
                        currentShape[length + 2] = position[2]
                        length = length + 2
                    else
                        error(('Bad "%s" command parameters: %s'):format(state, piece), 2)
                    end
                elseif lowerState == 'h' or lowerState == 'v' then
                    local axisIndex = (lowerState == 'h') and 1 or 2
                    if state == 'H' or state == 'V' then
                        position[axisIndex] = valueA
                    else
                        position[axisIndex] = position[axisIndex] + valueA
                    end
                    currentShape[length + 1] = position[1]
                    currentShape[length + 2] = position[2]
                    length = length + 2
                else
                    error('No active SVG drawing state', 2)
                end
            else
                error('Unsupported SVG draw command: '.. piece, 2)
            end
        end
    end
    return shapeData
end


local function makeRasterPolygon(shapeData, scaleX, scaleY)
    -- Default scale values if omitted.
    scaleX = scaleX or 1.0
    scaleY = scaleY or 1.0

    local rasterPolygon = {length=nil, width=nil, height=nil}

    local bbx1  = math.huge
    local bby1  = math.huge
    local bbx2 = -math.huge
    local bby2 = -math.huge

    local totalSegments = 0

    -- The p0 and p1 below are from "p1 = p0 + v . t"
    for shapeIndex = 1, #shapeData.shapes do
        local pointData = shapeData.shapes[shapeIndex]
        local p0 = {pointData[pointData.length - 1] * scaleX,
                    pointData[pointData.length] * scaleY}
        for pairIndex = 1, pointData.length, 2 do
            local p1 = {pointData[pairIndex] * scaleX,
                        pointData[pairIndex + 1] * scaleY}
            -- Find the bounding box.
            if p1[1] < bbx1 then
                bbx1 = p1[1]
            elseif p1[1] > bbx2 then
                bbx2 = p1[1]
            end
            if p1[2] < bby1 then
                bby1 = p1[2]
            elseif p1[2] > bby2 then
                bby2 = p1[2]
            end
            -- Store a new line segment object into the polygon table.
            local deltaX = p1[1] - p0[1]
            local deltaY = p1[2] - p0[2]
            local segmentData = {p0 = p0,
                                 p1 = p1,
                                 v = {deltaX, deltaY},
                                 lengthSq = (deltaX * deltaX + deltaY * deltaY)}
            totalSegments = totalSegments + 1
            rasterPolygon[totalSegments] = segmentData
            p0 = p1
        end
    end
    rasterPolygon.length = totalSegments
    rasterPolygon.width = bbx2
    rasterPolygon.height = bby2
    return rasterPolygon
end


-- Returns the (estimated) coverage of the polygon over the point, as a
-- value in the range [0.0, 1.0], with 1.0 being "fully covered".
local function sampleRasterPolygon(x, y, rasterPolygon)
    -- Sample from the pixel centers.
    x = x + 0.5
    y = y + 0.5

    local isInside = false
    local nearestDistance = math.huge
    local distanceTG = 0.0

    for segmentIndex = 1, rasterPolygon.length do
        local segmentData = rasterPolygon[segmentIndex]
        local p0 = segmentData.p0
        local p1 = segmentData.p1
        local v  = segmentData.v
        local deltaX = x - p0[1]
        local deltaY = y - p0[2]
        -- Only raycast on non-horizontal segments, and segments where
        -- the point is contained in the vertical span of the segment.
        -- This initial test condition is based on W. Randolph Franklin's
        -- point-in-poly algorithm (MIT licensed) from:
        -- https://wrfranklin.org/Research/Short_Notes/pnpoly.html#The%20C%20Code
        if ((p0[2] > y) ~= (p1[2] > y)) then
            local tX = deltaY / v[2]
            local intersectX = p0[1] + v[1] * tX
            if x < intersectX then
                isInside = not isInside
            end
        end

        local otherX, otherY
        local dot = (deltaX * v[1] + deltaY * v[2]) / segmentData.lengthSq
        if dot <= 0.0 then
            otherX = p0[1]
            otherY = p0[2]
        elseif dot >= 1.0 then
            otherX = p1[1]
            otherY = p1[2]
        else
            otherX = p0[1] + v[1] * dot
            otherY = p0[2] + v[2] * dot
        end
        local deltaX = x - otherX
        local deltaY = y - otherY
        local distance = math.sqrt(deltaX * deltaX + deltaY * deltaY)
        if distance < nearestDistance then
            nearestDistance = distance
            -- A pixel is shaped like a square, so there's two possible distances
            -- to its center: from its sides (half the square side) or from its
            -- corners (half the diagonal of the square).
            -- When coming from a corner to its center, that distance measures
            -- "half of the side, multiplied by the square root of two".
            --
            -- We find the slope ratio (like a tangent function) of the vector from
            -- the nearest point of the polygon towards the center of the pixel.
            -- This slope goes from 0.0 when it's orthogonal to the square sides, and
            -- up to 1.0 when it's orthogonal to the diagonals / square corners.
            -- Later this tangent value is used as a weight to mix between the
            -- "half-side" and "half-diagonal" lengths, so that the interpolated length
            -- is the reference length to estimate how far that the polygon is covering
            -- the square shape of the pixel.
            -- See 'baseDistance' below.
            deltaX = math.abs(deltaX)
            deltaY = math.abs(deltaY)
            if deltaX > deltaY then
                distanceTG = deltaX ~= 0.0 and (deltaY / deltaX) or 0.0
            else
                distanceTG = deltaY ~= 0.0 and (deltaX / deltaY) or 0.0
            end
        end
    end

    local CENTER_DISTANCE = 0.5
    -- Do a linear blending between 1.0 and sqrt(2), that is,
    -- a + (b - a) * t.
    -- Then use it to scale the half pixel distance, so it's in the
    -- range [0.5, 0.5 * sqrt(2)].
    local DIAG_OFFSET = 1.4142135623731 - 1.0
    local scaleFactor = 1.0 + DIAG_OFFSET * distanceTG
    local baseDistance = CENTER_DISTANCE * scaleFactor

    -- Map the nearest distance to the estimated "coverage" on the pixel, a
    -- value in the range [0.0, 1.0], in this way:
    --     - From 0.0 when the pixel square is fully outside the polygon;
    --     - Up to 0.5 when the pixel center is exactly at the polygon edge;
    --     - Up to 1.0 when the pixel square is fully inside the polygon.
    local coverage
    if isInside then
        coverage = (1.0 + nearestDistance / baseDistance) / 2.0
    else
        coverage = (1.0 - nearestDistance / baseDistance) / 2.0
    end
    -- Debug:
    --local coverage = isInside and 1.0 or 0.0
    -- Finally, clamp to the [0.0, 1.0] range
    return coverage < 0.0 and 0.0 or (coverage > 1.0 and 1.0 or coverage)
end


local function rasterizePolygon(rasterPolygon)
    local width = math.floor(rasterPolygon.width + 0.5)
    local height = math.floor(rasterPolygon.height + 0.5)
    local bytesPerPixel = 1
    local bytesPerRow = width * bytesPerPixel
    local data, ptr = makeByteData(height * bytesPerRow)

    for y = 0, height - 1 do
        local ptrOffset = y * bytesPerRow
        for x = 0, width - 1 do
            local fill = sampleRasterPolygon(x, y, rasterPolygon)
            local byteX = x * bytesPerPixel
            ptr[ptrOffset + byteX] = math.floor(fill * 255.0)
        end
    end

    local imageData = love.image.newImageData(width, height, 'r8', data)
    local image = love.graphics.newImage(imageData)
    image:setWrap('clamp', 'clamp')
    return image
end


function love.load()
    local shapeData = parseSVGDrawCommands(svgPolygonPointsString())
    local rasterPolygon = makeRasterPolygon(shapeData, 1.0, 1.0)
    local rasterPolygon3x = makeRasterPolygon(shapeData, 3.0, 3.0)

    love.window.setTitle('Polygon Rasterization Demo')
    local contentWidth  = rasterPolygon.width + rasterPolygon3x.width + 4 + 4 + 4
    local contentHeight = rasterPolygon3x.height + 4 + 4
    love.window.setMode(math.floor(contentWidth * 4.0 + 0.5),
                        math.floor(contentHeight * 4.0 + 0.5))

    love.graphics.setDefaultFilter('nearest', 'nearest')
    polygonImage1 = rasterizePolygon(rasterPolygon)
    polygonImage2 = rasterizePolygon(rasterPolygon3x)
    r8Shader = love.graphics.newShader(R8_PIXEL_SOURCE)
    love.graphics.setShader(r8Shader)
end


function love.draw()
    love.graphics.scale(4.0, 4.0)
    love.graphics.draw(polygonImage1, 4, 4)
    love.graphics.draw(polygonImage2, polygonImage1:getPixelWidth() + 4 + 4, 4)
end


function love.keypressed(key)
    if key == 'escape' then
        love.event.quit()
    end
end
Attachments
Raster_Polygon_Demo_v0.1.0.love
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User avatar
BrotSagtMist
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Joined: Fri Aug 06, 2021 10:30 pm

Re: Rasterizing polygons into images

Post by BrotSagtMist »

Cool tutorial, thanks for the effort.
obey
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dusoft
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Re: Rasterizing polygons into images

Post by dusoft »

Magic.
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darkfrei
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Joined: Sat Feb 08, 2020 11:09 pm

Re: Rasterizing polygons into images

Post by darkfrei »

Wow! Very nice!
I've tried to make the d-string parser, but it was always bad, there are too much variations how you can write the same vectors.
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RNavega
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Posts: 355
Joined: Sun Aug 16, 2020 1:28 pm

Re: Rasterizing polygons into images

Post by RNavega »

Wow, thanks guys!
darkfrei wrote: Wed Apr 17, 2024 7:15 am I've tried to make the d-string parser, but it was always bad, there are too much variations how you can write the same vectors.
Ah, mine is very simple and would probably fail too with some SVGs out in the wild. By the way, I was fascinated by your work on parabolas.

I was looking for a way to rasterize curves and arcs, so that you wouldn't have to flatten the drawings (which ends up adding more points to the polygons). After some initial reading on "scanline rendering", I now see that my rasterization attempt was done in a very brute-force way: for every pixel of the image, it loops through every segment of the polygon to see which has the nearest distance.
In a scanline renderer, it seems that a pre-processing step prepares things in slices so that it would make it much clearer what regions of the polygon would even be possible for a pixel to be covered by, making it fast to discard empty pixels that need no processing.

If I manage to find some articles / some resources on how to implement that, I'll update this.
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darkfrei
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Re: Rasterizing polygons into images

Post by darkfrei »

RNavega wrote: Fri Apr 19, 2024 12:30 am for every pixel of the image, it loops through every segment of the polygon to see which has the nearest distance.
I've made this exactly same way! But for not closed polyline:
viewtopic.php?p=243686#p243686

Image
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