How To ... Develop An SVG Polygon Renderer - Part 2

Step-By-Step

Code in Italic is the same as in Part 1, Code in Bold is new.

(
fn ColorToHex col =
(
	local theComponents = #(bit.intAsHex col.r, bit.intAsHex col.g, bit.intAsHex col.b)
	local theValue = "#"
	for i in theComponents do 
		theValue += (if i.count == 1 then "0" else "") + i
	theValue
)

fn compareFN v1 v2=
(
	if v1[6] < v2[6] then -1 else 1
)

This function will be used by the qsort() method to compare two elements of our sorting array.

We will be storing the Z-Depth value of each polygon in the 6th element of the array, so this function will get two array items and will return -1 or 1 depending on whether the first one is farther or closer than the second one.

local st = timestamp()
local theFileName = (getDir #userscripts + "\\PolygonRendering.svg")
local theSVGfile = createFile theFileName
format "<svg xmlns=\"http://www.w3.org/2000/svg\"\n" to:theSVGfile
format "\t\txmlns:xlink=\"http://www.w3.org/1999/xlink\">\n" to:theSVGfile

local theViewTM =  viewport.getTM()
theViewTM.row4 = [0,0,0]
local theViewTM2 = viewport.getTM()
local theViewSize = getViewSize()
local theViewScale = getViewSize()
theViewScale.x /= 1024.0
theViewScale.y /= 1024.0

local drawArray = #()

This array will be populated with the polygons including vertices transformed into view space, colors to use for Stroke and Fill, as well as the Z-Depth value for sorting.

local theStrokeThickness = 1

We will set the Stroke to 1 to be able to better investigate the previous problems at the outlines of the Geosphere.

gw.setTransform (matrix3 1)	
for o in Geometry where not o.isHiddenInVpt and classof o != TargetObject do
(
	local theStrokeColor = white
	local theFillColor = o.wirecolor	
	
	local theMesh = snapshotAsMesh o
	for f = 1 to theMesh.numfaces do
	(
		local theNormal = normalize (getfaceNormal theMesh f) 
		if (theNormal*theViewTM).z > 0 do
		(
			local theFace = getFace theMesh f
			local v1 = gw.transPoint (getVert theMesh theFace.x)
			local v2 = gw.transPoint (getVert theMesh theFace.y)
			local v3 = gw.transPoint (getVert theMesh theFace.z)
			
			v1.x /= theViewScale.x 
			v1.y /= theViewScale.y 
			v2.x /= theViewScale.x 
			v2.y /= theViewScale.y
			v3.x /= theViewScale.x
			v3.y /= theViewScale.y

			local theFaceCenter = meshop.getFaceCenter theMesh f
			local theZDepth = (theFaceCenter*theViewTM2).z 

We will sort by the distance of the Face Center to the viewer, so we need to get the Face Center position in World Space first, then transform it into View space.

The Z coordinate will be a negative value that will be lower the farther the point is from the viewer.

We will use this in our sorting function called by qsort()

			append drawArray #(v1, v2, v3, (ColorToHex theStrokeColor), (ColorToHex theLitFillColor), theZDepth)

Instead of outputting directly to the SVG file, we will collect each polygon in the drawArray variable, including the three vertices in screen space, the Hexadecimal colors of the polygon's Stroke and Fill, and the Z-Depth value calculated above.

		)--end if normal positive
	)--end f loop
)--end o loop

qsort drawArray compareFN

Now we can sort the drawArray according to the distance stored in the 6th element (the Z-Depth value).

We want polygons with lower Z-Depth (larger negative numbers) to be drawn first, thus implementing the "Painters Algorithm" where the drawing is performed back to front relative to the camera.

for d in drawArray do
(
	format "\t<polygon points='%,%  %,%  %,%' \n" d[1].x d[1].y d[2].x d[2].y d[3].x d[3].y to:theSVGfile
	format "\tstyle='stroke:%; fill:%; stroke-width:%'/>\n" d[4] d[5] theStrokeThickness to:theSVGfile
)

This for loop will output the sorted polygon data to the SVG file.

This is very similar to the previous version of the code, but we do this in a second loop and read the values from the sorted array.

format "</svg>\n" to:theSVGfile
close theSVGfile
local theSVGMap = VectorMap vectorFile:theFileName alphasource:0
local theBitmap = bitmap theViewSize.x theViewSize.y
renderMap theSVGMap into:theBitmap filter:true
display theBitmap
format "Render Time: % sec.\n" ((timestamp()-st)/1000.0)
)

Using The Script To Render Geometry

Let's test the changes to the script on the same examples as in Part 1 to see the difference.

As you can see, the problems at the edges of the Geosphere have been solved by the new sorted drawing approach.

It matches the results seen in the viewport using "Consistent Colors + Edged Faces" drawing mode pretty closely.

Let's increase the Stroke Thickness to 2 and render the Teapot primitive from the Part 1:

Let's resize the viewport and look at the result:

Rendering the problematic setup from the first part also produces correct results now:

But since we are culling the backfaces, it is possible to see the Sphere through the gap between the Teapot's Body and Lid.

By remarking the backface culling line

-- if (theNormal*theViewTM).z > 0 do

we can render all polygons of all objects without any culling. The rendering will take approximately twice as long, but the sphere will be correctly occluded: