Drawing an ellipse

[OldMoses]

This is a rough proof of concept sort of thing, but it does trace out an ellipse. By drawing the figure in quarters, I didn't deal with the headaches of line stepping, so I just used PSET. This makes the semi-major axis points spread out to leave gaps. Left & right mouse buttons drag the foci points, while the mouse wheel changes the base radius of the thing. Mostly vector math and distance formula, you won't find a single trig function. Which is why it's so damn long.

Code: (Select All)

'Vector Math Ellipse- OldMoses
TYPE V2
    x AS SINGLE
    y AS SINGLE
END TYPE

DIM AS V2 foci(1), fcomp(1), quad(3), origin, center, smaj, smin, smaj_n, smin_n, pt0, pt1, orth

SCREEN _NEWIMAGE(1024, 512, 32)

base_rad% = 100 '                                                   starting circle base radius
origin.x = 0: origin.y = 0 '
foci(0).x = 200: foci(0).y = 150
foci(1).x = 300: foci(1).y = 200

DO
    CLS
    WHILE _MOUSEINPUT
        base_rad% = base_rad% + _MOUSEWHEEL '                       base circle size
    WEND
    IF _MOUSEBUTTON(1) THEN R2_Mouse foci(0) '                      move foci(0) to left click position

    IF _MOUSEBUTTON(2) THEN R2_Mouse foci(1) '                      move foci(1) to right click position

    total% = _SHL(base_rad%, 1)

    R2_FCenter center, foci(0), foci(1) '                           compute center from foci data
    fcomp(0) = foci(0): R2_Add fcomp(0), center, -1 '               translate foci(0) relative to center as origin
    fcomp(1) = foci(1): R2_Add fcomp(1), center, -1 '               translate foci(1) relative to center as origin

    smaj = foci(0): R2_Add smaj, center, -1 '                       subtract foci from center to obtain semi-major axis vector <smaj>
    IF R2_Mag(smaj) = 0 THEN smaj.x = 1 '                           convert <smaj> to i-hat if <smaj> becomes a zero vector
    smin.x = smaj.y '                                               get minor axis orthogonal
    smin.y = -smaj.x

    FOR f% = 0 TO 1: CIRCLE (foci(f%).x, foci(f%).y), 3: NEXT f% '  draw marker circles at foci
    CIRCLE (center.x, center.y), 2 '                                draw marker circle at center
    'CIRCLE (center.x, center.y), base_rad% '                        draw base radius circle
    FOR x% = 1 TO base_rad% '                                       work along the semimajor axis one point at a time
        R2_Norm smaj, smaj, x% '                                    grow major axis vector
        R2_Norm smaj_n, smaj, -R2_Mag(smaj) '                       get its inverted twin
        flag = 0: m% = 0
        DO
            m% = m% + 1 '                                           grow an orthogonal <smin> from that point
            R2_Norm smin, smin, m%
            pt0 = smaj: R2_Add pt0, smin, 1: R2_Add pt0, fcomp(0), -1 '
            pt1 = smaj: R2_Add pt1, smin, 1: R2_Add pt1, fcomp(1), -1 '
            IF R2_Mag(pt0) + R2_Mag(pt1) >= total% THEN '           until its magnitude equals the hypotenuse to both foci
                R2_Norm smin_n, smin, -R2_Mag(smin) '               get its inverted twin
                flag = -1
            END IF
        LOOP UNTIL flag
        FOR curve% = 0 TO 3 '                                       plot point at each quadrant
            IF curve% MOD 2 = 0 THEN orth = smin ELSE orth = smin_n
            IF curve% > 1 THEN quad(curve%) = smaj_n ELSE quad(curve%) = smaj
            R2_Add quad(curve%), orth, 1 '                          add semi-major and semi-minor moves
            R2_Add quad(curve%), center, 1 '                        and add center position to result
            PSET (quad(curve%).x, quad(curve%).y), &HFFFF00FF '     plot the point
        NEXT curve%
    NEXT x%
    _DISPLAY
    _LIMIT 30
LOOP UNTIL _KEYDOWN(27)
END

SUB R2_Add (re AS V2, se AS V2, m AS SINGLE) 'Add a scalar multiple of <se> to <re>
    re.x = re.x + se.x * m
    re.y = re.y + se.y * m
END SUB 'R2_Add

SUB R2_FCenter (re AS V2, f AS V2, f1 AS V2) 'find center <re> between two points <f> & <f1>
    re = f1 '                                                       set center to second foci initially
    R2_Add re, f, -1 '                                              subtract first foci from center
    R2_Add re, re, -.5 '                                            subtract 1/2 of center from center
    R2_Add re, f, 1 '                                               add 1/2 center to first foci
END SUB 'R2_FCenter

FUNCTION R2_Mag! (v AS V2) 'Obtain magnitude of <v>
    R2_Mag! = _HYPOT(v.x, v.y)
END FUNCTION 'R2_Mag!

SUB R2_Mouse (re AS V2)
    re.x = _MOUSEX
    re.y = _MOUSEY
END SUB 'R2_Mouse

SUB R2_Norm (re AS V2, v AS V2, scalar AS INTEGER) 'grow <v> to scalar length <re>
    x! = v.x: y! = v.y
    m! = _HYPOT(x!, y!)
    IF m! = 0 THEN
        re.x = 0: re.y = 0
    ELSE
        re.x = (x! / m!) * scalar
        re.y = (y! / m!) * scalar
    END IF
END SUB 'R2_Norm