3D-PLOT

3D-PLOT renders a three-dimensional surface of the function z = 7·e^(−0.1(x²+y²)), a bell-curve-shaped “hat” function, using a perspective projection onto the TS 2068 screen. The plotting routine (lines 30–120) iterates over a grid from x=8 to −8 and y=−8 to 8 in steps of 0.5, applying a full rotation matrix with configurable theta and phi angles (both defaulting to 30°) and a viewing distance parameter. Hidden-line suppression is approximated using a `flag` variable: when a new scanline begins the pen is lifted, and subsequent points are connected with DRAW using PEEK 23677/23678 to read back the current plot coordinates, creating a wire-frame appearance. After a PAUSE, execution jumps to line 300, which displays an animated cosine wave pattern that grows progressively denser by incrementing the step size `i` in a loop, serving as a visual effect between runs.

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Program Structure

The program is divided into three logical sections:

1. Lines 10–120: Main 3D surface plotting loop, including the function definition and rendering pipeline.
2. Lines 130–190: Subroutines — clipping and draw logic (130–150), and initialization (160–190).
3. Lines 300–360: A standalone animated cosine-wave display, reached via GO TO 300 after the surface plot completes.

Mathematical Function

Line 10 defines FN z(x,y) = 7*EXP(-.1*(x*x+y*y)), a rotationally symmetric Gaussian (“Mexican hat” without the negative ring), peaking at 7 when x=y=0 and decaying outward. The grid spans x from 8 to −8 (step −1) and y from −8 to 8 (step 0.5), giving 17×33 = 561 sample points.

3D Perspective Projection

Lines 70–100 implement a full rotation and perspective transform. The angles theta and phi (both 30°) are converted to radians and cached as sn1, cn1, sn2, cn2 in the initialization subroutine (line 190), avoiding repeated trigonometric calls inside the loop. The projection equations are:

• ye — rotated Y component in eye space (line 70)
• ze — depth in eye space, offset by distance d=30 (line 80)
• xs — screen X with a 1.2 horizontal stretch and centering at 128 (line 90)
• ys — screen Y centered at 100 (line 100)

The scale factor s=2 and focal length 420 control the overall zoom. The 1.2 horizontal stretch on xs compensates for the non-square pixel aspect ratio of the display.

Hidden-Line Suppression via Flag and PEEK

The subroutine at lines 130–150 implements a simple hidden-line approximation. A flag variable tracks whether the pen is currently “down.” It is reset to 0 at the start of each x-row (line 40) and also whenever a point falls outside the screen boundary (line 130). The first valid point on a scanline is PLOTted and flag is set to 1 (line 140). Subsequent points are connected using DRAW, with the delta computed as xs - PEEK 23677 and ys - PEEK 23678 (line 150). System variables 23677 and 23678 hold the last PLOT/DRAW coordinates, allowing the program to avoid storing a separate previous-point variable.

Screen Clipping

Line 130 checks all four screen boundaries (xs<0, xs>255, ys<0, ys>175) before attempting to draw, preventing out-of-range PLOT/DRAW errors and resetting the pen flag so a new line segment begins after any gap.

Post-Plot Animation (Lines 300–360)

After a PAUSE 300, execution transfers to line 300 for an animated cosine display. A cosine wave is plotted across the screen width (0–255), and a diagonal line is also drawn from each point toward the center using DRAW 128-d, -80+f. The step variable i starts at 2 and increments by 1 each iteration; after each pass the screen is cleared and the loop restarts, producing a progressively coarser pattern. This section loops indefinitely via GO TO 320.

Key Variables

Variable	Role
d	Viewing distance (30) in 3D section; loop counter in cosine section
theta, phi	Rotation angles (30° each), converted to radians
sn1/cn1, sn2/cn2	Cached sin/cos of theta and phi
s	Scale factor for projection (2)
flag	Pen-up/pen-down state per x-row
xs, ys	Projected screen coordinates
i	Step increment for cosine animation

Notable Techniques

• Pre-computing all trigonometric values before the nested loop avoids expensive SIN/COS calls on every iteration.
• Using PEEK on the system’s last-plot coordinate variables eliminates the need for explicit previous-point tracking variables.
• The DEF FN at line 10 encapsulates the surface equation cleanly, making the function easy to substitute.
• The dual-use of variable d (viewing distance in section one, loop counter in section two) is a minor source of potential confusion if the two sections were ever combined differently.
• The cosine section uses both PLOT+DRAW for the wave and a second PLOT+DRAW for a radial line from the same point, creating a distinctive star-burst interference pattern as i grows.