**TI-84 Plus: Bézier Curves**

The Bézier Curve is defined as a set of parametric equations
of n points:

x(t) = ∑( nCr(n,r) * (1-t)^(n-k) * t^k * x_k ) from k = 0 to
n

y(t) = ∑( nCr(n,r) * (1-t)^(n-k) * t^k * y_k ) from k = 0 to
n

For 0 ≤ t ≤ 1

The curve fits points (x_0, y_0) (when t = 0) and (x_n, y_n)
(when t = 1). The degree of the
polynomial is n-1.

This blog covers the TI-84 Plus. I have a version for the TI nSpire and HP 50g
which can be found here:

The arguments given for the BEZIER program are two lists:
one of x-coordinates and one for y-coordinates.
The program switches to Parametric mode.

In order to accomplish this, I store lists to equation
variables, convert them to strings, and build a string to be converted to the
equation.

The commands Equ>String and String>Equ are found in
the catalog ([2

^{nd}] [ 0 ]). The DelVar command can handle one variable at a time. Temporary variables (XT5, YT5, XT6, YT6, Str7, Str8, Str9, Str0) are deleted at the end of the program to save space.**Program BEZIER**

Disp "BEZIER CURVE"

Input "X=",L₁

Input "Y=",L₂

If dim(L₁)≠dim(L₂)

Then

Disp "LISTS NOT SAME LENGTH"

Stop

End

Param

dim(L₁)→N

seq(K,K,0,N-1)→L₅

seq(N-K-1,K,0,N-1)→L₆

seq((N-1) nCr K,K,0,N-1)→L₄

L₄*L₁→L₃

L₄*L₂→L₄

"L₃"→X₅

_{T}:Equ>String(X₅_{T},Str7)
"L₄"→Y₅

_{T}:Equ>String(Y₅_{T},Str8)
"L₅"→X₆

_{T}:Equ>String(X₆_{T},Str9)
"L₆"→Y₆

_{T}:Equ>String(Y₆_{T},Str0)
"sum("+Str7+"*(1-T)^"+Str0+"*T^"+Str9+")"→X₁

_{T}
"sum("+Str8+"*(1-T)^"+Str0+"*T^"+Str9+")"→Y₁

_{T}
0→Tmin

1→Tmax

.05→Tstep

DelVar X₅

_{T}:DelVar Y₅_{T}
DelVar X₆

_{T}:DelVar Y₆_{T}
DelVar Str7:DelVar Str8

DelVar Str9:DelVar Str0

ZoomFit:Zoom Out

**Examples:**

Example 1: (0,0),
(1,2), (3,1)

X List: {0,1,3}

Y List: {0,2,1}

Example 2: (-2,4),
(0,0), (2,4), (4,2)

X List: {-2, 0, 2, 4}

Y List: {4, 0, 4, 2}

Example 3: (0, 10), (1, 6), (3, 3), (5, 8)

X List: {0, 1, 3, 5}

Y List: {10, 6, 3, 8}

This blog is property of Edward Shore. 2016