GRAPES USER'S MANUALGRAPES Ver 6.7

TOMODA Katsuhisa Dec 2010

a. OS Windows2000/XP/Vista Windows95/98/Me OS Ver6.16 b. 256MB 512MB c. SVGA800600 65000 16 d. 4MB

GRAPES GRAPES GRAPES GRAPES

URL http://www.osaka-kyoiku.ac.jp/~tomodak/grapes/

1 GRAPES1-1 GRAPESGRAPES 2

UNDO REDO

y = f ( x )

x, y

1-2 GRAPES GRAPES

6.70 (Shift_Jis)6.71 (Unicode) Unicode

GRAPES

GRAPES GRAPES .gpsGRAPES GRAPES GRAPES .gpp GRAPES

1-3

1. 2.

GRAPES *.gps GRAPES

GRAPES GRAPES Windows Vista GRAPES

2 2-1 1.

2.

3. OK

2-2

1. 2.

1. 2.

1. 2.

1. 2.

2-3 1. 2.

1. 2. 3. OK

2-4 14 14

a,b,c,d,k,m,n,p,q,s,t,u,v,

1 2 3 4

1 2 4 8

1. 2.

a b

2-5

1.

2.

3. OK

4.

off

3 3-1 1.

2. a. b. c.

Shift Ctrl 2

3-2 1.

2. a. b. c.

Shift Ctrl 1/2

3-3

1.

2. a. b. c.

3-4

11

1 1 UNDOREDO

1 1

1 1

UNDO UNDO

UNDO 200

REDO REDO

UNDO

3-5 /

y 1 -1 O -1 1 x

y 1

y

y

-1

O -1

1 x

O

x

O

x

y4 3

2 1 0 1

2 3 4 55 4 3 2 1 0 1 2 3 4

x

3-6

x x x x y y y y

1 2 5 10 1 1 1 1 2 5 10 , 2 , 90 , 180

1 2 3 6 9 18 45 90 1 1 1 1 1 1 1 1 2 3 6 9 18 45 90

Ctrl

3-7

5

x y 1 GRAPES x y 1 x 2 x 90 x

OK

3-8 1. 2.

xy x x

y = sin

1 2 5 10

3-9

150150 16001600

x, y

OK

4 4-1 1.

2.

3. 2-2 OKy4

3

2

1

4

3

2

1

O

1

2

3

4

x

1

2

3

4

4-2 1.

2.

3. OK

y4 3 2 1 4 3 2 1 O 1 2 3 4 1 2 3 4

x

4-3 and ( x 2 + y 2 2 2 ) and ( 1 < x + y 1 ) C1 : x 2 + y 2 2 2 , C2 : 1 < x + y 12 1

y2 1

O 1 2

1

2

x

C3 : C1 and C2

y

or ( x 2 + y 2 2 2 ) or ( 1 < x + y 1 ) C1 : x 2 + y 2 2 2 , C2 : 1 < x + y 12 1

2 1

O 1 2

1

2

x

C3 : C1 or C2 andor and 1(C1 or C2) and C3 2C1 or (C2 and C3) C1 or C2 and C3

x 2 + y 2 < 2 2 y2

y2

1

1

2

1

O

1

2

x

2

1

O

1

2

x

1

1

2

2

4-4 y = f ( x )

10

x , y 10 10

x = tan y x cos y = sin y

5 5-1 1. 2.

3.

4.

x

5.

y

6.

7. OK

5-7

5-2 x 1. x

2.

y 1. y

2.

1. 2. 2-2

1. 2.

5-3 1.

2.

3.

4. OK

5.

=0

=1

=2 =3

5-4 3

y2 1

y2

1

P2

1

0.2

P2

O

x

O

x

1. 2. y

2 1

P2

O

x

O 2 x y 2 1

1. 2.

5-5 1.

2.

3.

4. x, y

5. r

6. 2-2 7.

8. OK

y 2 1 O P 2 x

5-6 1.

2.

3.

4. y

5.

6. 2-2 7.

8. OK

5-7 1. 2. 3. 4. 5. OK3 2 1

1. 2. a. b.

6-1 10

6 6-1 1. 2.

3.

4.

x

5.

y

6. a. b.

7. 8. GRAPES 5000 9. 2-2 10. 11. 12. OK

y2 1 O 1 2 3 x

P

6-2

1. 2.

1. 2.

1. 2.

6-3 1. 2.

3.

4.

r

5.

6.

7. OK

P

O

2

4 x

6-4 r x 0 ( r , ) = ( r , + ) r > 0 r < 0

r

x |r|

x

O

x

O

x

r = sin 2

6-5 , r

1.

2.

3. r

4.

y

1

O

1

x

1

0 < 2 <

7 7-1 1.

2.

3. a. b. c.

4.

5. OK

7-2 1.

2.

3. OK

P

P

P

P

P

P

Q

Q

Q

Q

Q

Q

7-3 3 3 PQR

1.

2. 2 P, Q P Q

3.

4. R 5.

6.

7. OK

7-4 3 PQR PQR

1. 2. P, Q

3. 4. R

5.

6. 7. OK

PQR QP

QR 180

7-5 1. PQ 2. 3. !{[PQ]}

4.

1. 2. 3. !{[arg(P,Q,R)]|3} 4. 5.

8 8-1 f ( x )

1.

2.

f , g ,h , f1 ,8

, f5

y = f (x ) y = f ( x p ) + q

y f(x,y) f (2x , k) = 0 y f (x) = f (x , 0) x, y, z, w 4 f ( x, y, z, w)

8-2 y2

y1 = sin ax , y 2 = cos bx

1

O 1

y 3 = sin ax + cos bx 2

2

3 2

2

x

y 3 = y1 + y 2 y1 y 2

y

2

1

O 1

2

3 2

2

x

y1 = y 2 + y 3

2

y 2 = sin ax y 3 = cos bx

8-3

A

1. A 5-7

2. A ( A.x , A.y ) A y = a ( x A.x ) 2 + A.y

3. A

8-4

1. A, B, C A, B, C

2. A, B, C 7-3

3. G A, B, C ( A.x , A.y ), ( B.x , B.y ), ( C.x , C.y ) G

A.x + B.x + C.x A.y + B.y + C.y , 3 3

4. G

ABC 9

9 9-1 ABC G

A.x + B.x + C.x A.y + B.y + C.y , 3 3

OA + OB + OC 3 GRAPES

OA + OB + OC A + B + C 3 3GRAPES

2 x 2 y 3

(2,3) .x .y

( 2 , 3 ).x = 2 ( 2 , 3 ).y = 3

P, Q PQ PQ

9-2 x y

ABC

1. G

2.

3.

4. ABC

5. OK

y5 4 3 2 1 O

A

G B C1 2 3 4 5

x

9-3

P + ( 4,5)

P ( 4 , 5) ( 2 , 3 ) ( 4 , 5) PQ A,B

(2,3) ( 4,5) 3 PQ ( A + B) / 2

* ( 1, 2 ) (3 , 4) ( 1, 2 ) ( 3 , 4 )

[ ] | (3,4) | ( 3 , 4 )

[PQ] PQ PQ PQ PQ

9-4 lenlen ( P , Q ) P, Q P

len ( P )

len ( P , (2 , 3) ) P ( 2 , 3 ) len ( 2 , 3 )( 2 , 3 )

argarg ( P , Q , R ) PQR arg ( P , Q ) arg ( P ) POQ OP

0 2

det ( P , Q )2

9-5 ( P , Q , m , n ) PQ m : n ( P , Q ) PQ

mid

( A , B , C , D ) AB CD ( A , B , C , r ) AB C r intr 2 ( B , A , C , r )AA P

C

P B

C B

( A , B , C , r )

( B , A , C , r )

( A , a , B , b ) A a B b 2 ( B , b , A , a )

( P , A , B ) P AB perp ( P , A , B ) perpL

(A, B, C) ABC Gcentr Gcentr Ccentr Hcentr Icentr Ecentr Crad Irad (A,B,C) (A,B,C) (A,B,C) (A,B,C) (A,B,C) (A,B,C) (A,B,C)

( A , C , t ) A C t ( A , t ) ( A ) A t A 90

rot

roll( t ) (cos t , sin t ) ( a , ) roll a roll( )

unit (P) OP

(t , P1 , P2 ,

, Pn ) n 0 t < n n 20 , Pn ) = Pk

polygon

k (k 1 , P1 , P2 ,

t = t0 + k n k (t , P1 , ( n , P1 ,

, Pn ) = (t0 , P1 , , Pn ) = ( 0 , P1 ,

, Pn ) , Pn )

X ( x , y ) x , y X ( x, y ) XA = 3 A 3 y5 4 3

A2 1 2 1 O 1 1 2 3 4

x

9-6

f ( x, y ) = 2 x + 3 y

f (4,5) = 2 4 + 3 5 P = ( 4 , 5 )

f ( P) = 2 4 + 3 5

X ( x , y ) f ( x, y ) = 2 x + 3 y 2 x + 3 y = ( 2,3) ( x, y )

f ( x, y ) = ( 2 , 3 ) X Y ( z , w )

f ( x ) = x A + (1 x ) B f ( x ) AB

f ( x, y ) = ( a x + b y , c x + d y ) GRAPES f ( x, y ) = f (( x, y ))

Q = f ( P) Q P f ( x, y , z, w) = f (( x, y ), ( z, w))

9-7

GRAPES x y

P

P = 2

P = 2 P = ( 2, 0)

9-8 P * Q

e i = cos + i sin

i i a + b i = a + b ( 0, 1) = ( a, b)

= ( 0, 1)

1 (1) = i 1 i Sqrt()

exp, sin , cos , tan, sinh, cosh, tanh, sol sol

sol ( x4 = 16 , 1) = 2 , sol ( x4 = 16 , 2) = 2

sol ( x4 = 16 , 3) = ( 0, 2) , sol ( x4 = 16 , 4) = ( 0, 2)conj P = ( 1, 2) conj (P) = ( 1, 2) conj

conj

10 10-1

1.

2.

3.

4.

5. OK

a. b. c. d. 10

10-2

1. 2. 3.

10-3 Sqrt(1-x^2)/4

1 x 2 4 { }

!{ }

{Sqrt(2)} 2 !{Sqrt(2)} 2 1.4142

| !{Sqrt(a)|8} a

10-4 a , b y = ax + b

a = 3 , b = 2 y = 3x 2 {y=ax+b} y = ax + b a b {y=!{a}x+!{b}} !{b}+b

6 2( x 1) 3 ?{ 2 ( x 1) 3 } 3 P, Q, R 2 y1 = path( x, P, Q, R )

y

R P2

Q2 O 2

x

10-5 Black, Blue, Green, Red, Purple, Gray 6 rrggbb 3 16 FF0000 FFFF00 v{ } / 10-6 2 10 10-7 10-8 GRAPES 1. 2. 3. 4. OK 10-9 GRAPES6.70 unicode $1FFF Times New Roman MS P GRAPES 11 11-1 GRAPES 200 10 1. 2. 3. GRAPES y// Del l j x 1 y 2 z 3 2 3 l = 2 , j = 3 , x = 2.5 , y = 6 z = 8.5 4. OK OK 1. l j x 1 y 2 z 3 w 1 Cells(,) 2. y Tab Shift+Tab Enter 11-2 Shift+ ESC & Ctrl+C Ctrl+X Ctrl+V &Undo 11-3 Cells(, ) CellsP(, ) 2 x y 1. 2. 3. 1 4. 5. OK 6. OK 11-4 Cells(, ) := Cells(1,2) := 4 2 Cells(1,2) := (4,5) Cells(1,2) := 4 , Cells(1,3) := 5 2 CellsP(, ) := ClrAllCells 20 Cells( 1 , 1 ) := Cells( 2 , 1 ) := For n := 3 to 1 1 20Cells( n , 1 ) := Cells( n1 , 1 ) + Cells( n2 , 1 ) NextCells() 1 Cells() = Cells(1) Cells( 1 ) Cells( 2 ) For := := 1 1 20 Cells( n1 ) + Cells( n2 )n := 3 toCells( n ) := Next 14 12 12-1 4-4 1/1 1/2 1/4 1/8 sin x + sin y = sin 3x + sin 3 y x y 100% 75% 50% 25% 0% 12-2 0 9-7 (x, y) log log ln arg arg 0 < 2 < () 4 9 12-3 GRAPES sin( 2 x ) sin 2 x sin x , cos x , tan x A sin x , A cos x , A tan x exp( x ) e x log x log(a, x ) a x ln( x ) sinh x , cosh x , tanh x x 3 x Sqrt , Cbrtint(x ) round(x) frc(x) frc(x) = x - int(x)|x| abs( x ) | | [ ] sign( x) rnd( x ) 0 x x = 1 0 1 ( x ) , ( x, y ) f ( x ) , g ( x ), h( x ), f 1( x )f 5( x ) f ' ( x ) f 5 ' ( x ) f ' ' ( x ) f 5' ' ( x ) F ( x )F 5( x ) F ( x ) = f (t ) d t0 x f (x ) 8 nCr(x,y ) gcd(x,y ) lcm(x,y ) f ( x, y ) f ( x, y , z ) f ( x, y, z, w) g , h, f 1 f 5 Max ( x1 ,, xn ) , Min( x1 ,, xn ) 1 20 Cells(m, n) m n 1 Cells(m) = Cells(m,1)rgb( r, g , b) 24 r, g, b Red, Green, Blue 01 rgb(1,0,0) rgb(1,1,0) rgb(0.5,0.5,0.5) hsl(h,s, l ) 24 h, s, l 01 h hsl( h+1 , s , l ) = hsl( h , s , l )hsl(0,1,0.5) hsl(0,1,0.8) hsl(0,0,0.5) 0h1 11sl00area(x) (area(0) , area(1)) (area(2) , area(3))Pressed(Virtual key code) true1 false windows 12-4 x !x degree .x , .y x y .r y1y 20 P , Q O X (x , y) r , r = len( x, y ) = arg( x, y )sol ( f ( x ) = g ( x ) , n ) 4 f ( x ) = g ( x ) n n = 1, 2, 3, 4 n n = 1 cof (n , f ( x )) f (x ) 6 n cof ( 2 , ( x 2) 3 ) = 6() Sumkk =152 ( k ,1, 5 , k 2 ) x () Product x () Igr 0sin 2 x dx ( x , 0 , , sin 2 x ) x x Stepsize()12-5 path ( x , P1 ,, Pn ) n ( n1 ) | P | len( P) | [ ] |len( P1 , P2 ) arg(P) 0 arg < 2 , arg < arg( P1 , P2 ) P1OP2arg( P1 , P2 , P3 ) P1 P2 P3det(a, b, c, d) a d b c det( P , Q ) P.x Q.y P.y Q.x(P , A, B) P AB perpL (A, B, C) ABC Crad (A, B, C) ABC Iradroll( t ) (cos t , sin t ) P(n) n P, Q, , V, A, ,N 1, 2, 3, , 21unit(P) OP (A, B, C) ABC Gcentr (A, B, C) ABC Ccentr (A, B, C) ABC Hcentr (A, B, C) ABC Icentr (A, B, C) ABC Ecentr (B, C, A) (C, A, B) (A, B, C, D) AB,CD intr (A, B, C, r ) AB C r 2 (B, A, C, r ) ( A, a, B, b ) A a B b 2 ( B , b , A , a ) (P, A, B) P AB perp ( A, B) AB mid( A, B, m, n) AB m : n ( P) P 90 rot ( P, t ) P t ( P, C, t ) P C t ( t , P1 , P2 ,, Pn ) : n 0 t < n n 20 polygonproj( x, y, z, s, t , d ) ( x, y, z ) s, t, d d = 0 d 9-6 12-6 x ^ y = x y x < 0 y sin n x = (sin x ) n x mod y > , , < , , = , true false y = x ( x 0) x 0 and , or , not true false : * & a,b,c,d,k,m,n,p,q,s,t,u,v, x, y, z, w z, w X( x , y ) Y( z , w ) e 12-7 and or sin , cos , tan , Asin , Acos , Atan , log ,,3 sin a cos x 2 + 1 = (sin a )(cos x 2 ) + 1sin a ( x + 1) 2 + 1 = sin (a ( x + 1) 2 ) + 1sin a ( x + 1) 2 + 1 = (sin a )( x + 1) 2 + 1 2n ! = 2 ( n ! ) , 2 a x 2 = 2a ( x 2 ) GRAPES 12-8 (1) y = 2 x 4 x x + 23 2(2) y = 1 + 2 x2x3 2 / 3 x (3) y =2x +5(4) y = log 2 ( x 1)(5) y = 2 x 4 x x + 23 2(6) y = e 2 sin 4 xx12-9 y = x 2 ( x 0) y = sin x ( t x t + 1 )t x t 1 (t x ) and ( x t + 1) x 2 ( x < 1) y= 2 x ( x 1)y = x 2 ( x < 1) or ( 2 x )( x 1) or y 3 = y1( x < 1) or y 2( x 1) 12-10 GRAPES 1. f ( x ) = x 2 2 x 2. f ' , g ' , h ' y 2 = f ' ( a )( x a ) + f (a ) 2 8 1. f ( x ) = x 2 2 x 2. F, G, H F (x ) f (t ) d t 0x 13 13-1 1. 2. 1. 2. 13-2 x x x 1.x 2. x x x x 1. 2. 13-3 2 / 1. 2. 4 9 200 13-4 13-5 y1y1 2O 1 2 x 2O 1 2 x22 13-6 bmp, jpg, gif, png, emf, wmf 3 GRAPES GRAPES 14 14-1 GRAPES 1. 2. 3. 4. OK 1 // 1 HideScript // Draw sin, Sqrt, Pi 20 14-2 x , y , z , w if ~ then ~ if ~ then ~ else ~ for ~ next while ~ wend DrawOverDraw Calc RefreshRefreshSticker SetColor SetLineColor SetInnerColor ClrAImg ClrAImgData SetAImg AImgOn, AImgOff ShowObj HideObj/ InvShowObj SetArea Play , PlayAfterPlaySync SetSampleRate on ~ change SetTme Wait Pause end Call HideScript14-3 On change 2 On Change On a, b Change : a, b F1 14-4 4 x , y , z , w A x B x 2 X , Y X (x , y) = (x , y) X Y = (z , w) X = (1 , 2)x := 1 y := 2 CALL CALL //Sum a := x+y C void Sum( x , y , z , w); {a=x+y} x , y , z , w := := := 1 0 := a := sin t := P := (2,3) P.x := 2 P := (2,3) P(s,t) s := 2 t := 3 P := P, Q, R, , V, A, B, ,N 1, 2, 3, , 7 , 8, 9, , 21P(2) := (2,3) P(n) := (2,3)Q := (2,3) := x := tan t Cells(, ) := Cells(1,2) := 4 / a 2 Cells(1,2) := (4,5) Cells(1,2) := 4 , Cells(1,3) := 5 1 CellsP(, ) := ClrAllCells Inc DecIncDec Inc() Dec() Inc(a)14-5 for nextfornext for next for := to step next step while wendwhile wend while wendif then if then if then endifif then else if then else if then else endif14-6 Draw Draw: Draw Calc OverDrawDraw Draw Calc Draw Refresh Calc: Draw OverDraw RefreshCalc Refresh Calc Refresh Draw Draw RefreshSticher 14-7 SetColor() RGB 24 GRAPES 16 rgbhsl SetColor(y1 , rgb(0.8, 0, 1)) y1 SetLineColor() SetInsideColor()14-8 ClrAImg()ClrAImg ClrAImgClear After Images ClrAImg() ClrAImg(y1,C2,P,L2) y1 C1 P L2 ClrAImg ClrAImgData ClrAImgData( ) Draw Refresh SetAImg14-9 AImgOn AImgOffAImgOff OFF AImgOn ShowObj()HideObj()InvShowObj()HideObj() HideObj(y1,C2,P,L2) y1 C1 P L2 ShowObj() InvShowObj() SetArea(x1,y1,x2,y2)2 x1,y1,x2,y2 14-10 Play() 16 22,050Hz Play( t , 0 , 2 , sin880Pit) "Pit" 440Hz Play( t , 0 , 2 , (sin 880Pit , sin 882Pit)) 440Hz 441Hz GRAPES x Play Play PlayAfter Wave Wave PlayAfter()PlayAfter Wave Wave PlayAfter Wave Wave Play Play() PlayAfter Play PlayAfter( t , 0 , 1 , sin400Pit) PlayAfter( t , 0 , 2 , sin600Pit) Play 200Hz 1 300Hz 2 PlaySync()Play Play PlaySync SetSampleRate() 48,000Hz SetSampleRate(48,000) GRAPES wave 480,000 16 GRAPES 10 10 32768 32767 wave 14-11 SetTime() WaitSetTime Wait SetTime(n) a := 3 Draw Wait //SetTime n Wait()PausePause() Pause()pausepause()OK Call( , 1 , 2 , 3 , 4 ) Call 4 x , y , z , w 2 2 Call(test , (1,2),(3,4))Call(test , (1,2),3,4) Call(test , 1,2,(3,4))Call(test , 1,2,3,4) Call(test , 1,(2,3),4) End Call on changeP, Q 2 on a,b,f change a,b f a t // on a change t := 0 calc ClrAImg on change 15 15-1 TIPS 10, 5, 2, 1/2, 1/5, 1/10 15-2 1. 2. 3. B/W GRAPES 4. OK1. 2. B/W Shift 15-3 Windows Bitmap*.bmp Jpeg*.jpg Gif (*.gif), Png (*.png), Enhanced Metafile*.emf Windows Metafile*.wmfEnhanced Metafile Windows Metafile 1. 2. Image Image000Image001Image002Image003Image004 Play 15-4 / 15-5 2 1. 2. 3. 4.