Sunday, July 1, 2018

Casio fx-CG 50 and HP Prime: Pyramid Constructed by Points


Casio fx-CG 50 and HP Prime:  Pyramid Constructed by Points



The program PYRAPTS calculates the surface area and volume of a pyramid that is defined by its vertex points.  The program assumes all the points of its base lies on the plane z = 0, and there is only one tip point.

All of the base points, B1, B2, B3, B4, etc., are entered as two coordinates, one list for the X coordinates and the other for the corresponding Y coordinates.  Keep in mind that for this program, all of its base points lie on the plane Z=0.

The coordinates for the tip point, T, are prompted separately. 

Casio fx-CG 50 Program PYRAPTS (text file)

'ProgramMode:RUN
"2018-06-24 EWS"
ClrText
Red Locate 1,1,"FOR THE BASE, Z=0"
For 1->J To 1000
Next
"X _List _"?->List 1
"Y _List _"?->List 2
Dim List 1->N
"TIP X COORD="?->X
"TIP Y COORD="?->Y
"TIP Z COORD="?->Z
0->S
List 1[1]*List 2[N]-List 1[N]*List 2[1]->R
For 2->J To N
R+List 1[J]*List 2[J-1]-List 1[J-1]*List 2[J]->R
Sqrt(Z^<2>+(Y-List 2[J])^<2>+(X-List 1[J])^<2>)->A
Sqrt(Z^<2>+(Y-List 2[J-1])^<2>+(X-List 1[J-1])^<2>)->B
Sqrt((List 2[J]-List 2[J-1])^<2>+(List 1[J]-List 1[J-1])^<2>)->C
(A+B+C)/2->H
S+Sqrt(H(H-A)(H-B)(H-C))->S
Next
Abs R/2->R
S+R->S
RZ/3->V
ClrText
Blue Locate 1,1,"SURFACE AREA="
Red Locate 1,2,S
Blue Locate 1,4,"VOLUME="
Red Locate 1,5,V

Notes:
1.  - >  is the storage arrow →
2.  ^<2> is the square key x^2
3.  If you type in the program manually, the line ‘ProgramMode:RUN is not needed
4.  _ represents the space key

HP Prime Program PYRAPTS

EXPORT PYRAPTS()
BEGIN

// 2018-06-25 EWS
// pyramid by points

LOCAL L1,L2,X,Y,Z;
LOCAL S,V,R,J,N;

INPUT({{L1,[[6]]},
{L2,[[6]]}},"Base Points: Z=0",
{"X List:","Y List:"});

N:=SIZE(L1);

INPUT({X,Y,Z},"Tip Coordinates",
{"X: ","Y: ","Z: "});

S:=0;
R:=L1(1)*L2(N)-L1(N)*L2(1);

FOR J FROM 2 TO N DO
R:=R+L1(J)*L2(J-1)-L1(J-1)*L2(J);
A:=√(Z^2+(Y-L2(J))^2+
(X-L1(J))^2);
B:=√(Z^2+(Y-L2(J-1))^2
+(X-L1(J-1))^2);
C:=√((L2(J)-L2(J-1))^2
+(L1(J)-L1(J-1))^2);
H:=(A+B+C)/2;
S:=S+√(H*(H-A)*(H-B)*(H-C));
END;

R:=ABS(R)/2;
S:=S+R;
V:=R*Z/3;

PRINT();
PRINT("Surface Area: "+S);
PRINT("Volume: "+V);
RETURN {S,V};

END;

Example

Base points:  (0,0,0),  (3,4,0),  (-3,4,0)  (z=0 is implied for base points)
Tip point:  (0,1,√2)

Input:
List X:  {0, 3, -3}
List Y:  {0, 4, 4}
Tip X: 0
Tip Y: 1
Tip Z: √2

Results:
Surface Area: 25.7904472451
Volume:  5.65685424947

Eddie

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