DrawArcWedge

Display; ModifyGraph width={Aspect,1}   // make a square graph so that a circle is a circle
SetDrawEnv fillfgc= (47872,47872,47872); DrawArcWedge(0.5, 0.5, 0.25, 0.45, 150, 210) // a grey "c"
SetDrawEnv fillfgc= (65280,43520,0); DrawArcWedge(0.5, 0.5, -0.25, 0.45, 60, 120)  // an orange fan

// DrawArcWedge draws an arced wedge, i.e. a polygon delimited by two concentric arcs.
// Origin = (x0, y0), Arc1 = (r1, phi1-->phi2), Arc2 = (r2, phi2-->phi1), the arcs are connected by lines.
// If one of the radii is 0, you get a pizza wedge. If r1==r2, it's just an arc. If r1*r2 < 0, it's a fan.
// The coordinate system is similar to DrawArc: 0° is at 3 o'clock, the angle is counterclockwise.
// No choice is made for the drawing coordinate system, you have to set it up with SetDrawEnv.

// To try out DrawArcWedge without the overhead of the other functions in this proc file, use:
//  Display; ModifyGraph width={Aspect,1}   // make a square graph so that a circle is a circle
//  SetDrawEnv fillfgc= (47872,47872,47872); DrawArcWedge(0.5, 0.5, 0.25, 0.45, 150, 210) // a grey "c"
//  SetDrawEnv fillfgc= (65280,43520,0); DrawArcWedge(0.5, 0.5, -0.25, 0.45, 60, 120)  // an orange fan
// (the easy way: select the three lines above, choose "Decommentize" (Edit menu), then hit "Ctrl+Enter")  

function DrawArcWedge(x0, y0, r1, r2, phi1, phi2)
variable x0, y0, r1, r2, phi1, phi2

    // 1. set up basic variables ("hard-wired" section)
    variable rad = 180 / pi     // sin() and cos() need radians, not degrees
    variable dphi = phi2 - phi1 // difference angle, might be zero
    variable intphi = 5         // use approx 5° intervals between polygon points in arcs
    variable nphi = max( floor(dphi / intphi), 1 )  // number of arc points - 1
                            // "max(.., 1)" prevents division by zero (short arcs also need two end points)
    dphi /= nphi                // (interval for the arc points) = (difference angle) / (number of arc points - 1)

    // 2. draw the ArcWedge
    // 2.1 draw the first point on radius r1, at angle phi1
    variable angle = phi1 / rad
    variable x1 = r1*cos(angle), y1 = -r1*sin(angle)    // note: this implements the coordinate system of DrawArc
    DrawPoly x0+x1, y0+y1, 1, 1, {x1, y1}   // use an unnamed polygon instead of a wave pair to make each ArcWedge unique

    // 2.2 draw the arc on radius r2, from angle phi1 to phi2 (implicitely creates line from r1 to r2, at phi1)
    variable k, kmax
    kmax = nphi * ( r2 != 0 )       // 1st arc at r2 (only one point iff r2 == 0)
    for( k = 0; k <= kmax; k += 1 ) // integers are better for the loop to prevent rounding errors
        angle = (phi1 + k*dphi) / rad
        DrawPoly/A {r2*cos(angle), -r2*sin(angle)}
    endfor

    // 2.3 draw the arc on radius r1, from angle phi2 to phi1 (implicitely creates line from r2 to r1, at phi2)
    kmax = nphi * ( r1 != 0 )       // 2nd arc at r1 (only one point iff r1 == 0)
    for( k = 0; k <= kmax; k += 1 )
        angle = (phi2 - k*dphi) / rad   // note: loop direction inverted
        DrawPoly/A {r1*cos(angle), -r1*sin(angle)}
    endfor
end