Part Seven Notes: Working by hand. ie; Pen, Paper and Calculator

I have drawn out the map on graph paper. The map consists of a single spiralling strand of asteroids, here we see a top elevation of the spiral. This spiral will be made up of a long chain of straight cylinders, all lying end to end.Doing this by hand can be tricky, but its not impossible. Ok, lets work through this.

fig One - Top Elevation

Marking in the cylinder lines

On the map above (fig One) each square in the grid and for the moment I am using at a scale of 10000 (10km) here. I never usually write on a scale because I so often change it once I have seen the map in the game.

I drew out the spiral using a compass, drawing half a circle, then extending the circumference slightly and moving the point of origin so the spiral was a constant line. The innermost halfcircle with a radius = 10k has it's centre at 0,-10000,0. The second halfcircle has its centre at 0,0,0 and a radius of 20000 (20km), the third half circle has its centre at 0,-10000,0 and a radius of 30000 (30km), and so on.

So, we have all our pretty spiral design, its just a matter of translating it into coordinates and putting these coordinates into the Resouresphere file. Ok, we will be using cylinders, which are in fact straight lines, so we need to set up our straight lines using this spiral as our reference. For those of you condemned to work by hand/calculator etc, I will show you what I mean and how to do it; Lets look a little more closely at the Second quadrant of this graph:

fig Two - Quadrant II

Ok, The centre of our map is Point O. First thing i did was draw a line between Point O and the very corner of the map (Point A). This Line (Line OA) will neatly split the circular lines (the Spiral) half way between Point C and Point F. So drawing in Line OA we get the half way point in each of the quarter circles we can see in this quadrant.

Starting with the outer most circlular line of the spiral, at the moment, we can see the spiral is bisected at Point B. Next I drew in Line CB. This looks way off the circlular template we are using so i further split the line in two by measuring (with a ruler) exactly halfway along line CB, to get Point D Next i drew in the Line OD and extrapolated it further until it bisects the outermost part of the spiral at Point E, making it Line OE. Lastly I drew in the Lines CE and EB to give me a better fit for the circular nature we are trying to adopt here.

I would then need to repeat this to get a straight line for every part of the circle throughout the map, and you can see that our points are already there, its just a matter of drawing in the lines, ie for Lines BH and HF then dropping down to the next part of the visible spiral. You can see (although i have not marked them on the graph) that the points you need are already there, where the lines OE, OA and OH bisect each circular line (the spiral), thats your start/end point for each cylinder.

Coordinates for each line.

What you need to do now is to get the coordinates for each line. The best way to do this is by using the coordinates where each line meets rather than using the graph and reading directly the coordinates for the centre of each line (which is easier I grant you, but you get better looking results where each cylinder meets if you do it the hard way. Trust me).

Remember this must be done in 3D, our spiral will be dropping downwards, so all our lines must be measured in 3D we do this by working out the angle and length in 2D, then work out the angle and length for the Z shift (up/down). Then putting the two together and measuring the angle of the line and its rotation about both Y and Z axis.

I'm doing this from memory and I really cant say for sure how accurate this is.. Lets look at line CE. Point C is coordinates -80000,0,56000 and Point E is coordinates -74000,30000,58000 converting this into a right angled triangle we can see the hypotenuse (X) will be at point -74000,0,56000. from this we get the following:

fig Three - Line CE

Where Point Y is the coordinates ,-74000,30000,56000, this point is directly below Point E and so triangle CXY is a flat 2D triangle. So using these coordinates, and armed with our knowledge of trigonemetry we can work out the length of CE, (Which will be the length of our cylinder), the halfway point of Line CE (which will be our cylinder coordinates), the angle of XCY (which will be our cylinders rotz (angle about Z) angle) and the angle CEY which will be the roty (angle about Y) angle). Everything you need it there. As long as you know your trig.

I honestly can't tell you exactly how to do all this because I dont remember, I don't know my trig... There are a couple help files available with the Primer, written by people who do, you can see an Introduction to Trigonometry here and a More In-Depth Discussion on Trigonometry here. My Advice? Get Excel.

Yeah right!

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