While I was waiting for some equipment to continue my presentation of the Vectrex gaming console, I was looking for a simple but neat application to write today. Something that is not obvious as a game, and useful for my next post. That’s when it hit me: **Bézier curves**! The Vectrex BIOS has routines to display dots and segments, but nothing to handle parametric curves. And what a shame, especially if you consider that Bézier curves – a particular case of **B-Splines** – are at the core of modern vector packages such as **vector fonts**, **PostScript**, illustration software such as **CorelDraw!** or **Adobe Illustrator**, etc.

As you may know, **Pierre Étienne Bézier** is a French engineer who used these parametric curves to model car body parts at **Renault**. In other words, how can anyone live today without Bézier curves? So, I went ahead and used the **Vectres32** cartridge to write a simple *draw_bezier_curve()* function that plots a cubic Bézier curve in BASIC. To illustrate the use of the function, I’ve also written a simple driver code that creates the **cubic Bézier curve**, moves around the anchor and control points, and accepts input from the joystick to dynamically change the **number of steps** used to draw the curve.

You can see a few runs of this demo in the videos and pictures attached to this post. I also added the source code so you and check it out if you are interested. I will use this code for my last post dedicated to the Vectrex console. I hope that by then, you will appreciate how advanced this little system was when it hit the US market in 1982. Enjoy!

## bezier.bas

' bezier.bas: draws a Bezier curve, use joystip up & down top change draw step. ' Define display configuration. scale = 80 intensity = 70 frame_rate = 20 ' Define various UI configuration. anchor_size = 4 control_size = 1 instructions = { _ {-50, 90, "INSTRUCTIONS"}, _ {-80, 80, "JOYSTICK UP TO +1 BEZIER STEPS"}, _ {-80, 70, "JOYSTICK DOWN TO -1 BEZIER STEPS"}, _ {-80, 60, "MIN STEP IS 1 - MAX STEP IS 80."} _ } ' Bn functions are respectively first, second, third and fourth ' Bernstein derivations to compute the quadratic B-Spline. function B1(t) return ((t) * (t) * (t)) endfunction function B2(t) return (3 * (t) * (t) * (1 - (t))) endfunction function B3(t) return (3 * (t) * (1 - (t)) * (1 - (t))) endfunction function B4(t) return ((1 - (t)) * (1 - (t)) * (1 - (t))) endfunction sub draw_square(x, y, s) move = MoveSprite(x, y) square = LinesSprite( _ { _ { MoveTo, s, s }, _ { DrawTo, -s, s}, _ { DrawTo, -s, -s }, _ { DrawTo, s, -s }, _ { DrawTo, s, s } _ } _ ) call ReturnToOriginSprite() endsub sub draw_segment(x1, y1, x2, y2) segment = LinesSprite( _ { _ { MoveTo, x1, y1 }, _ { DrawTo + $F0, x2, y2} _ } _ ) call ReturnToOriginSprite() endsub sub draw_bezier_curve(x1, y1, x2, y2, x3, y3, x4, y4, s) if s > 0.0 then call ReturnToOriginSprite() call draw_square(x1+anchor_size, y1, anchor_size) call draw_square(x2, y2, control_size) call draw_segment(x1+anchor_size, y1, x2, y2) call draw_square(x3, y3, control_size) call draw_square(x4, y4, anchor_size) call draw_segment(x3, y3, x4, y4) i = 0.0 lastx = x4 lasty = y4 d = 1.0 / s; curve = {{ MoveTo, x1, y1 }} repeat x = Int(x1 * B1(i) + x2 * B2(i) + x3 * B3(i) + x4 * B4(i)) y = Int(y1 * B1(i) + y2 * B2(i) + y3 * B3(i) + y4 * B4(i)) move = {{ MoveTo, lastx, lasty}, { DrawTo, x, y }} curve = AppendArrays(curve, move) i = i + d lastx = x lasty = y until i >= 1.0 move = {{ DrawTo, x1, y1 }} curve = AppendArrays(curve, move) bezier = LinesSprite(curve) endif endsub ' Driver code to demonstrate use of draw_bezier_curve(). x = 4 o = 80.0 s = 20 sd = 1 sil = 1 sul = 80 while true d = 0 for i = -50.0 to 50.0 step x ' Display instructions. textSize = {25, 4} '{40, 5} call TextSizeSprite(textSize) call TextListSprite(instructions) ' Display current steps. textSize = {40, 5} current_steps = {{-50, 150, "STEPS: " + s}} call TextSizeSprite(textSize) call TextListSprite(current_steps) ' Setup display for the Bezier curve. call IntensitySprite(intensity) call SetFrameRate(frame_rate) call ScaleSprite(scale) ' Draw the updated Bezier curve. call draw_bezier_curve( _ -o, -d, _ -o+d, o+d, _ o-d/4, -o, _ o-1.5*d, o-d, _ s _ ) ' Prepare for next frame & update steps -- if needed. d = d + 5 controls = WaitForFrame(JoystickDigital, Controller1, JoystickY) if controls[1, 2] > 0 then s = s + sd if s > sul then s = sul endif elseif controls[1, 2] < 0 then s = s - sd if s < sil then s = sil endif endif call ClearScreen() call ReturnToOriginSprite() next i endwhile