added rotation to the lib. just turn the device a little bit...and don't forget to check this out: pinch and two-finger-drag-function
Code: Select all
/*
'c'-description
'y'-testing
'b'-definitions
''
'c'
returns the "x"- and "y"-coordinate of a point on the ipad-screen. Basis is a user-defined coordinate-system given by xmin, xmax, ymin, ymax
===========
global Variables
===========
xmin:smallest number of x-range within new coordinate system
xmax:biggest number of x-range
ymin:smallest number of y-range
ymax:biggest number of y-range
by omitting one pair (e.g.:ymin,ymax) those values are then calculated with respect to screen ratio
==========
functions
==========
tc_x(x):
transforms "x"-user-coordinate into "x"-coordinate of ipad-screen. usable with DRAW LINE etc.
When using PIXEL then call function as:2*tc_x(x) etc.
"sizes" within user-defined system like "width" or "height" must be treated like :
SIZE tc_x(10)-tc_x(0) which corresponds to SIZE 10
x: "x"-coordinate within user-defined coordinate-system
----------
btc_x(x):
inverse function of tc_x(x).
returns the "x"-coordinate of the user-defined coordinate-system. Basis is the corresponding point on ipad-screen. e.g. usable when transforming touch-information into user-defined -coordinates
x: x-value of the screen
----------
tc_y(y):
analogue
----------
btc_y(y):
analogue
----------
draw_sys():
draws the two axis of the user-defined coordinate-system
----------
draw_ticks(tick_x,tick_y):
draws ticks in a user-defined coordinate-system
tick_x: x-value of interval for each tick
tick_y: analogue
----------
draw_grid(dx,dy):
draws a grid in a defined coordinate-system
dx: x-value of interval
dy: analogue
----------
get_unit_x():
returns the smallest element on x-scale in respect of displayable points and params xmin, xmax
(note: DRAW-command etc. NOT PIXEL-command
----------
get_unit_y():
analogue
----------
get_ratio():
returns ratio: dy/dx
----------
pinch(touch0_x,touch0_y,touch1_x,touch1_y)
to use with:
GET TOUCH 0 AS touch0_x, touch0_y
GET TOUCH 1 AS touch1_x, touch1_y
in the main-program (for time-efficiency)
returns -1 if at least one finger has been released
returns 1 if both fingers on screen
changes the global variables: xmin,xmax,ymin,ymax
''
*/
'y'
test2:
GRAPHICS
REFRESH OFF
GET ORIENTATION p
SET ORIENTATION p
xmin=-5
xmax=5
'ymin=-5
'ymax=5
OPTION ANGLE DEGREES
DRAW SIZE 2
'r'
test2loop:
'y'
tau=-(ATAN2(ACCEL_Y(),ACCEL_X())-ATAN2(1,0))
GET TOUCH 0 AS touch0_x, touch0_y
GET TOUCH 1 AS touch1_x, touch1_y
pinch(touch0_x,touch0_y,touch1_x,touch1_y)
GRAPHICS CLEAR .5,.5,.5
DRAW COLOR 1,1,1
draw_sysr(tau)
draw_ticksr(1,1,tau)
'DRAW LINE tc_x(0),tc_y(0) TO tc_x(1),tc_y(0)
DRAW COLOR 1,0,0
DRAW LINE tcr_x(0,0,tau),tcr_y(0,0,tau) TO tcr_x(3,1,tau),tcr_y(3,1,tau)
REFRESH
GOTO test2loop
RETURN 'of test2
''
'b'
DEF tcr_x(x,y,tau)
RETURN tc_x(rot_x(x,y,tau))
END DEF
'=================
DEF tcr_y(x,y,tau)
RETURN tc_y(rot_y(x,y,tau))
END DEF
'=================
DEF rot_x(x,y,tau)
phi=ATAN2(y,x)
r=SQR(x*x+y*y)
RETURN r*COS(phi+tau)
END DEF
'=================
DEF rot_y(x,y,tau)
phi=ATAN2(y,x)
r=SQR(x*x+y*y)
RETURN r*SIN(phi+tau)
END DEF
'=================
DEF tc_x(x)
'calculate min& max values when those are left to zero respecting screen-ratio
IF .ymin=0 AND .ymax=0 THEN
.ymin=.xmin*SCREEN_HEIGHT()/SCREEN_WIDTH() ! .ymax=.xmax*SCREEN_HEIGHT()/SCREEN_WIDTH()
ENDIF
IF .xmin=0 AND .xmax=0 THEN
.xmin=.ymin*SCREEN_WIDTH()/SCREEN_HEIGHT() ! .xmax=.ymax*SCREEN_WIDTH()/SCREEN_HEIGHT()
ENDIF
'calculate gradient, linear transormation function
mx=SCREEN_WIDTH() /(.xmax-.xmin)
x0=(-1)*.xmin*mx
tc_x=x*mx+x0
END DEF
'=================
DEF tc_y(y)
IF .ymin=0 AND .ymax=0 THEN
.ymin=.xmin*SCREEN_HEIGHT()/SCREEN_WIDTH() ! .ymax=.xmax*SCREEN_HEIGHT()/SCREEN_WIDTH()
ENDIF
IF .xmin=0 AND .xmax=0 THEN
.xmin=.ymin*SCREEN_WIDTH()/SCREEN_HEIGHT() ! .xmax=.ymax*SCREEN_WIDTH()/SCREEN_HEIGHT()
ENDIF
my=SCREEN_HEIGHT() / (.ymin-.ymax)
y0=(-1)*.ymax*my
tc_y=y*my+y0
END DEF
'=================
DEF btc_x(x)
'back-transformation
IF .ymin=0 AND .ymax=0 THEN
.ymin=.xmin*SCREEN_HEIGHT()/SCREEN_WIDTH() ! .ymax=.xmax*SCREEN_HEIGHT()/SCREEN_WIDTH()
ENDIF
IF .xmin=0 AND .xmax=0 THEN
.xmin=.ymin*SCREEN_WIDTH()/SCREEN_HEIGHT() ! .xmax=.ymax*SCREEN_WIDTH()/SCREEN_HEIGHT()
ENDIF
mx=SCREEN_WIDTH() /(.xmax-.xmin)
x0=(-1)*.xmin*mx
btc_x=(x-x0)/mx
END DEF
'=================
DEF btc_y(y)
IF .ymin=0 AND .ymax=0 THEN
.ymin=.xmin*SCREEN_HEIGHT()/SCREEN_WIDTH() ! .ymax=.xmax*SCREEN_HEIGHT()/SCREEN_WIDTH()
ENDIF
IF .xmin=0 AND .xmax=0 THEN
.xmin=.ymin*SCREEN_WIDTH()/SCREEN_HEIGHT() ! .xmax=.ymax*SCREEN_WIDTH()/SCREEN_HEIGHT()
ENDIF
my=SCREEN_HEIGHT() / (.ymin-.ymax)
y0=(-1)*.ymax*my
btc_y=(y-y0)/my
END DEF
'=================
DEF btc_x2(x)
'back-transformation
mx=SCREEN_WIDTH() /(pinch.xmax-pinch.xmin)
x0=(-1)*pinch.xmin*mx
btc_x2=(x-x0)/mx
END DEF
'=================
DEF btc_y2(y)
my=SCREEN_HEIGHT() / (pinch.ymin-pinch.ymax)
y0=(-1)*pinch.ymax*my
btc_y2=(y-y0)/my
END DEF
'=================
DEF draw_sysr(tau)
IF .ymin=0 AND .ymax=0 THEN
.ymin=.xmin*SCREEN_HEIGHT()/SCREEN_WIDTH() ! .ymax=.xmax*SCREEN_HEIGHT()/SCREEN_WIDTH()
ENDIF
IF .xmin=0 AND .xmax=0 THEN
.xmin=.ymin*SCREEN_WIDTH()/SCREEN_HEIGHT() ! .xmax=.ymax*SCREEN_WIDTH()/SCREEN_HEIGHT()
ENDIF
DRAW LINE tcr_x(.xmin,0,tau),tcr_y(.xmin,0,tau) TO tcr_x(.xmax,0,tau),tcr_y(.xmax,0,tau)
DRAW LINE tcr_x(0,.ymin,tau),tcr_y(0,.ymin,tau) TO tcr_x(0,.ymax,tau),tcr_y(0,.ymax,tau)
END DEF
'=================
DEF draw_sys()
IF .ymin=0 AND .ymax=0 THEN
.ymin=.xmin*SCREEN_HEIGHT()/SCREEN_WIDTH() ! .ymax=.xmax*SCREEN_HEIGHT()/SCREEN_WIDTH()
ENDIF
IF .xmin=0 AND .xmax=0 THEN
.xmin=.ymin*SCREEN_WIDTH()/SCREEN_HEIGHT() ! .xmax=.ymax*SCREEN_WIDTH()/SCREEN_HEIGHT()
ENDIF
DRAW LINE tc_x(.xmin),tc_y(0) TO tc_x(.xmax),tc_y(0)
DRAW LINE tc_x(0),tc_y(.ymin) TO tc_x(0),tc_y(.ymax)
END DEF
'=================
DEF draw_ticks(tick_x,tick_y)
IF .ymin=0 AND .ymax=0 THEN
.ymin=.xmin*SCREEN_HEIGHT()/SCREEN_WIDTH() ! .ymax=.xmax*SCREEN_HEIGHT()/SCREEN_WIDTH()
ENDIF
IF .xmin=0 AND .xmax=0 THEN
.xmin=.ymin*SCREEN_WIDTH()/SCREEN_HEIGHT() ! .xmax=.ymax*SCREEN_WIDTH()/SCREEN_HEIGHT()
ENDIF
FOR n=tick_x TO .xmax STEP tick_x
DRAW LINE tc_x(n),tc_y(0)-5 TO tc_x(n), tc_y(0)+5
NEXT n
FOR n= -tick_x TO .xmin STEP -tick_x
DRAW LINE tc_x(n),tc_y(0)-5 TO tc_x(n), tc_y(0)+5
NEXT n
FOR n=tick_y TO .yMAX STEP tick_y
DRAW LINE tc_x(0)-5,tc_y(n) TO tc_x(0)+5, tc_y(n)
NEXT n
FOR n=-tick_y TO .ymin STEP -tick_y
DRAW LINE tc_x(0)-5,tc_y(n) TO tc_x(0)+5, tc_y(n)
NEXT n
END DEF
'=================
DEF draw_ticksr(tick_x,tick_y,tau)
IF .ymin=0 AND .ymax=0 THEN
.ymin=.xmin*SCREEN_HEIGHT()/SCREEN_WIDTH() ! .ymax=.xmax*SCREEN_HEIGHT()/SCREEN_WIDTH()
ENDIF
IF .xmin=0 AND .xmax=0 THEN
.xmin=.ymin*SCREEN_WIDTH()/SCREEN_HEIGHT() ! .xmax=.ymax*SCREEN_WIDTH()/SCREEN_HEIGHT()
ENDIF
FOR n=tick_x TO .xmax STEP tick_x
DRAW LINE tcr_x(n,-5*get_unit_y,tau),tcr_y(n,-5*get_unit_y,tau) TO tcr_x(n,5*get_unit_y,tau), tcr_y(n,5*get_unit_y,tau)
NEXT n
FOR n= -tick_x TO .xmin STEP -tick_x
DRAW LINE tcr_x(n,-5*get_unit_y,tau),tcr_y(n,-5*get_unit_y,tau) TO tcr_x(n,5*get_unit_y,tau), tcr_y(n,5*get_unit_y,tau)
NEXT n
FOR n=tick_y TO .yMAX STEP tick_y
DRAW LINE tcr_x(-5*get_unit_x,n,tau),tcr_y(-5*get_unit_x,n,tau) TO tcr_x(5*get_unit_x,n,tau), tcr_y(5*get_unit_x,n,tau)
NEXT n
FOR n=-tick_y TO .ymin STEP -tick_y
DRAW LINE tcr_x(-5*get_unit_x,n,tau),tcr_y(-5*get_unit_x,n,tau) TO tcr_x(5*get_unit_x,n,tau), tcr_y(5*get_unit_x,n,tau)
NEXT n
END DEF
'=================
DEF draw_grid(d_x, d_y)
IF .ymin=0 AND .ymax=0 THEN
.ymin=.xmin*SCREEN_HEIGHT()/SCREEN_WIDTH() ! .ymax=.xmax*SCREEN_HEIGHT()/SCREEN_WIDTH()
ENDIF
IF .xmin=0 AND .xmax=0 THEN
.xmin=.ymin*SCREEN_WIDTH()/SCREEN_HEIGHT() ! .xmax=.ymax*SCREEN_WIDTH()/SCREEN_HEIGHT()
ENDIF
FOR x=d_x TO .xmax STEP d_x
DRAW LINE tc_x(x),tc_y(.ymin) TO tc_x(x), tc_y(.ymax)
NEXT x
FOR x=d_x TO .xmin STEP -d_x
DRAW LINE tc_x(x),tc_y(.ymin) TO tc_x(x), tc_y(.ymax)
NEXT x
FOR y=d_y TO .ymax STEP d_y
DRAW LINE tc_x(.xmin),tc_y(y) TO tc_x(.xmax),tc_y(y)
NEXT y
FOR y=d_y TO .ymin STEP -d_y
DRAW LINE tc_x(.xmin),tc_y(y) TO tc_x(.xmax),tc_y(y)
NEXT y
END DEF
'=================
DEF get_unit_x
IF .ymin=0 AND .ymax=0 THEN
.ymin=.xmin*SCREEN_HEIGHT()/SCREEN_WIDTH() ! .ymax=.xmax*SCREEN_HEIGHT()/SCREEN_WIDTH()
ENDIF
IF .xmin=0 AND .xmax=0 THEN
.xmin=.ymin*SCREEN_WIDTH()/SCREEN_HEIGHT() ! .xmax=.ymax*SCREEN_WIDTH()/SCREEN_HEIGHT()
ENDIF
get_unit_x= (.xmax-.xmin)/SCREEN_WIDTH()
END DEF
'=================
DEF get_unit_y
IF .ymin=0 AND .ymax=0 THEN
.ymin=.xmin*SCREEN_HEIGHT()/SCREEN_WIDTH() ! .ymax=.xmax*SCREEN_HEIGHT()/SCREEN_WIDTH()
ENDIF
IF .xmin=0 AND .xmax=0 THEN
.xmin=.ymin*SCREEN_WIDTH()/SCREEN_HEIGHT() ! .xmax=.ymax*SCREEN_WIDTH()/SCREEN_HEIGHT()
ENDIF
get_unit_y= (.ymax-.ymin)/SCREEN_HEIGHT()
END DEF
'=================
DEF get_ratio
IF .ymin=0 AND .ymax=0 THEN
.ymin=.xmin*SCREEN_HEIGHT()/SCREEN_WIDTH() ! .ymax=.xmax*SCREEN_HEIGHT()/SCREEN_WIDTH()
ENDIF
IF .xmin=0 AND .xmax=0 THEN
.xmin=.ymin*SCREEN_WIDTH()/SCREEN_HEIGHT() ! .xmax=.ymax*SCREEN_WIDTH()/SCREEN_HEIGHT()
ENDIF
get_ratio= (.ymax-.ymin)/(.xmax-.xmin)
END DEF
'=================
DEF pinch(t0_x,t0_y,t1_x,t1_y)
IF old_pinch=0 AND t1_x>0 THEN 'new touch with 2 fingers?
old_pinch=1
xmin=.xmin ! xmax=.xmax ! ymin=.ymin ! ymax=.ymax
t0_x_first=btc_x2(t0_x) ! t0_y_first=btc_y2(t0_y) ! t1_x_first=btc_x2(t1_x) ! t1_y_first=btc_y2(t1_y)
ENDIF
IF t1_x<0 OR t0_x<0 THEN 'finger released?
old_pinch=0
RETURN -1
ENDIF
t0_x_last=btc_x2(t0_x) ! t0_y_last=btc_y2(t0_y) ! t1_x_last=btc_x2(t1_x) ! t1_y_last=btc_y2(t1_y)
.xmin=xmin+(MIN(t0_x_first,t1_x_first)-MIN(t0_x_last,t1_x_last))
.xmax=xmax+(MAX(t0_x_first,t1_x_first)-MAX(t0_x_last,t1_x_last))
.ymax=ymax+(MAX(t0_y_first,t1_y_first)-MAX(t0_y_last,t1_y_last))
.ymin=ymin+(MIN(t0_y_first,t1_y_first)-MIN(t0_y_last,t1_y_last))
RETURN 1
END DEF
'=================
/*
DEF follow_c(z(),v(),alph_max,z1) 'returns complex number of position
index=OPTION_BASE()
v_bearing=
END DEF
*/
'===========included maths=============
'returns a string of length L with random letters from a...z
DEF str_rnd$(L)
letter$=""
FOR n=1 TO l
letter$= letter$&CHR$(i_rnd(ASC("a"),ASC("z")))
NEXT n
RETURN letter$
END DEF
'returns a random number between [a...b] only once by calling the function until all numbers have been returned
'returns -1 when all numbers have been returned
'control = 1: creates tupple of numbers [a...b]
'control=0: returns randomly a number of above created tupples and removes it
DEF t_rnd(a,b,control)
OPTION SORT DESCENDING
optionbase=OPTION_BASE()
IF control=1 THEN 'new
num_elements=b-a+1
DIM m(num_elements)
n=0
WHILE n<num_elements
m(n+optionbase)=a
a=a+1
n=n+1
END WHILE
ENDIF
IF control=0 THEN 'return rnd and reduce
IF num_elements=0 THEN RETURN -1
SORT m
random=RND(num_elements)+optionbase
number=m(random)
m(random)=0
num_elements=num_elements-1
'DEBUG PAUSE
RETURN number
ENDIF
END DEF
'==========
DEF i_rnd(a,b) 'returns random integer between two given numbers [a,b]
i_rnd=FLOOR((b+1-a) *RND(1)+a)
END DEF
'==========
DEF r_rnd(a,b) 'returns random real number between two given real numbers (a,b)
r_rnd=(b-a)*RND(1)+a
END DEF
'==========
DEF phi_vector(x1,y1,x2,y2) 'angle phi of a vector defined by two points
delta_y=y2-y1 ! delta_x=x2-x1
phi_vector=ATAN2(delta_y,delta_x)
END DEF
'==========
DEF phi_vectors(v1x1,v1y1,v1x2,v1y2,v2x1,v2y1,v2x2,v2y2) 'v1 to v2 in mathematical sense
phi_vectors=phi_vector(v2x1,v2y1,v2x2,v2y2)-phi_vector(v1x1,v1y1,v1x2,v1y2)
END DEF
'==========
'returns the distance to the nearest number (grid*n+anchor) of a where n is a natural number. (e.g. glueing-to-grid-function of a with c as anchor and b as the gridsize around that anchored point.
DEF nearest(a,grid,anchor)
grid=ABS(grid)
IF grid-(ABS(a-anchor)%grid)>(ABS(a-anchor)%grid) THEN
'ifthen=1
nearest=-1*SIGN(a-anchor)*(ABS(a-anchor)%grid)
ELSE
'ifthen=2
nearest=SIGN(a-anchor)*(grid-(ABS(a-anchor)%grid))
ENDIF
'IF b-((a-anchor)%b)>((a-anchor)%b) THEN nearest=-1*((a-anchor)%b) ELSE nearest=b-((a-anchor)%b)
END DEF
'===========
'returns the nearest number to a with a grid and its anchor
DEF nearest2(a,grid,anchor)
grid=ABS(grid)
IF grid-(ABS(a-anchor)%grid)>(ABS(a-anchor)%grid) THEN
'ifthen=1
nearest2=-1*SIGN(a-anchor)*(ABS(a-anchor)%grid)+a
ELSE
'ifthen=2
nearest2=SIGN(a-anchor)*(grid-(ABS(a-anchor)%grid))+a
ENDIF
END DEF
'==========
'returns the gridposition of a within the grid anchored in anchor. gridpos of anchor = 0
'difference to nearest2(...): this function counts the "gridlines" to 'a' while nearest2 returns the distance
DEF gridpos(a,grid,anchor)
grid=ABS(grid)
IF grid-(ABS(a-anchor)%grid)>(ABS(a-anchor)%grid) THEN
m_nearest=-1*SIGN(a-anchor)*(ABS(a-anchor)%grid)+a
ELSE
m_nearest=SIGN(a-anchor)*(grid-(ABS(a-anchor)%grid))+a
ENDIF
gridpos=(m_nearest-anchor)/grid
END DEF
'==========
'returns the number related to gridposition n dependent on gridsize (grid) and anchor. complementary of nearest2.
DEF nextn(n,grid,anchor)
n=INT(n)
nextn=anchor+grid*n
END DEF
'==========
'returns the nth value of a line with length starting in anchor and divided in a number of sections num_section
DEF divide(anchor,length,num_section,n)
length_section=length/num_section
divide= length_section*n+anchor
END DEF
'==========
DEF point_on_orthog(px,py,lpx1,lpy1,lpx2,lpy2)
IF (lpx1=lpx2 AND lpy1<>lpy2) OR (lpx1<>lpx2 AND lpy1=lpy2) THEN
'orthogonal and no point instead of line
IF lpx1=lpx2 THEN
'senkrechte
IF px=lpx1 AND py>=MIN(lpy1,lpy2) AND py<=MAX(lpy1,lpy2) THEN RETURN (py-lpy1)/(lpy2-lpy1)
ELSE
'waagrechte
IF py=lpy1 AND px>=MIN(lpx1,lpx2) AND px<=MAX(lpx1,lpx2) THEN RETURN (px-lpx1)/(lpx2-lpx1)
ENDIF
RETURN -1
ELSE 'not orthogonal
RETURN -1
ENDIF
END DEF
'==========
'returns -1 if point is off line. otherweise returns a value between [0,1] equivalent to the relation to the length of the line
DEF point_on_line(px,py,lpx1,lpy1,lpx2,lpy2)
d_ly=lpy2-lpy1 ! d_lx=lpx2-lpx1
m=(d_ly)/(d_lx) 'gradient of the line
IF px-lpx1<>0 THEN 'check division by zero
IF m<>(py-lpy1)/(px-lpx1) THEN
RETURN -1
ELSE
point_line_relation=(py-lpy1)/d_ly 'actual calculation of relation
RETURN point_line_relation
ENDIF
ELSE 'divisor = 0
IF py-lpy1=0 THEN RETURN 0 'd_x and d_y=0 so point is in the origin of the line
ENDIF
END DEF
'============
DEF length_line(lpx1,lpy1,lpx2,lpy2)
d_y=lpy2-lpy1 ! d_x=lpx2-lpx1
length=SQR(d_y*d_y+d_x*d_x)
RETURN length
END DEF
'============
'returns point on the line px with distance lambda from origin of line (lpx1,lpy1). lambda=1 is length of line.
DEF px_to_line(lambda,lpx1,lpy1,lpx2,lpy2)
d_x=lpx2-lpx1
px=d_x*lambda+lpx1
RETURN px
END DEF
'============
'analogue
DEF py_to_line(lambda,lpx1,lpy1,lpx2,lpy2)
d_y=lpy2-lpy1
py=d_y*lambda+lpy1
RETURN py
END DEF
'============
'counts the occurrances of a sub$ within a string$
'"xx" in "xxxx" will be counted as 2
DEF count_instr(string$,SUB$)
_base_=OPTION_BASE()
result=INSTR(string$,SUB$)
IF result=-1 THEN RETURN 0
IF result=LEN(string$)-LEN(SUB$)+_base_ THEN RETURN 1
RETURN 1+ count_instr(MID$(string$,result+LEN(SUB$)),SUB$)
END DEF
'============
'returns the number of data separated by separator$
'";" will be counted as 2 (";" is separator)
'"asd" will be counted as 1 (";" is separator)
DEF lensepstr(string$,separator$)
RETURN count_instr(string$,separator$)+1
END DEF
'============
'returns a substring within a given string$ with trenn$ as separator and thus dividing the string in sections
DEF insepstr$(section,s1$,S2$)
IF MAX(LEN(s1$),LEN(s2$))=LEN(s1$) THEN 's1 the longest?
separator$=s2$ ! string$=s1$ 'shortest is separator
ELSE
string$=s2$ ! separator$=s1$
ENDIF
IF string$="" THEN RETURN "ERROR" '-1 problematisch bei der auswertung. Stoppzeichen definieren und übergeben?
'insepstr$(2,",","123,4567,890") -> 4567
option_base_=OPTION_BASE()
OPTION BASE 1
length=LEN(string$)
IF INSTR(string$,separator$,1)=-1 AND section=1 THEN RETURN string$ '-1 'trennzeichen nicht vorhanden
pos2=0
FOR n= 1 TO section
pos1=pos2+1
IF pos1<=LEN(string$) THEN pos2=INSTR(string$,separator$,pos1) ELSE RETURN "ERROR" '-1
IF pos2 = -1 THEN BREAK 'letztes komma fehlt
NEXT n
IF n=section AND pos1<=length THEN pos2=length+1 'letzte komma fehlt
IF n<section THEN RETURN "ERROR" '-1 'weniger sections als erwartet
'(n=section und noch zeichen übrig: letztes komma fehlt, sonst zuwenig sections
RETURN MID$(string$,pos1,pos2-pos1)
OPTION BASE option_base_
END DEF
'===========
'returns x-coordinate of x-ing point of to orthogonal lines.returns -1e30 if no intersection
DEF orthog_cross_x(L1x1,L1y1,L1x2,L1y2,L2x1,L2y1,L2x2,L2y2)
L1(1,1)=L1x1
L1(1,2)=L1y1
L1(2,1)=L1x2
L1(2,2)=L1y2
L2(1,1)=L2x1
L2(1,2)=L2y1
L2(2,1)=L2x2
L2(2,2)=L2y2
IF L1(1,1)=L1(2,1) THEN bool(1)=1
IF L1(1,2)=L1(2,2) THEN bool(2)=1
IF L2(1,1)=L2(2,1) THEN bool(3)=1
IF L2(1,2)=L2(2,2) THEN bool(4)=1
IF (bool(1)=0 AND bool(2)=1 AND bool(3)=1 AND bool(4)=0) OR (bool(1)=1 AND bool(2)=0 AND bool(3)=0 AND bool(4)=1) THEN
'orthogonal
IF bool(1)=1 THEN
x=L1(1,1) ! y=L2(1,2)
ELSE
x=L2(1,1) ! y=L1(1,2)
ENDIF
'now check if point is on one line
IF point_on_orthog(x,y,L1x1,L1y1,L1x2,L1y2)>0 AND point_on_orthog(x,y,L2x1,L2y1,L2x2,L2y2)>0 THEN RETURN x
ELSE 'not orthogonal
RETURN -1e308
ENDIF
END DEF
'===========
'returns x-coordinate of x-ing point of to orthogonal lines.returns -1e30 if no intersection
DEF orthog_cross_y(L1x1,L1y1,L1x2,L1y2,L2x1,L2y1,L2x2,L2y2)
L1(1,1)=L1x1
L1(1,2)=L1y1
L1(2,1)=L1x2
L1(2,2)=L1y2
L2(1,1)=L2x1
L2(1,2)=L2y1
L2(2,1)=L2x2
L2(2,2)=L2y2
IF L1(1,1)=L1(2,1) THEN bool(1)=1
IF L1(1,2)=L1(2,2) THEN bool(2)=1
IF L2(1,1)=L2(2,1) THEN bool(3)=1
IF L2(1,2)=L2(2,2) THEN bool(4)=1
IF (bool(1)=0 AND bool(2)=1 AND bool(3)=1 AND bool(4)=0) OR (bool(1)=1 AND bool(2)=0 AND bool(3)=0 AND bool(4)=1) THEN
'orthogonal
IF bool(1)=1 THEN
x=L1(1,1) ! y=L2(1,2)
ELSE
x=L2(1,1) ! y=L1(1,2)
ENDIF
'now check if point is on one line
IF point_on_orthog(x,y,L1x1,L1y1,L1x2,L1y2)>0 AND point_on_orthog(x,y,L2x1,L2y1,L2x2,L2y2)>0 THEN RETURN y
ELSE 'not orthogonal
RETURN -1e308
ENDIF
END DEF
'==========
DEF dist_to_horizontal(px,py,lpx1,lpy1,lpx2,lpy2)
IF lpx1<>lpx2 AND lpy1=lpy2 THEN
'horizontal
IF px>=MIN(lpx1,lpx2) AND px<=MAX(lpx1,lpx2) THEN RETURN py-lpy1 ELSE RETURN -1 'pos if point overhead else neg.
ELSE
'not horizontal
RETURN -1
ENDIF
END DEF
'==========
'remark. generalisation of this problem: turn line(lp2) and point (p) around lp1 then perp_to_orthog
DEF dist_to_vertical(px,py,lpx1,lpy1,lpx2,lpy2)
IF lpy1<>lpy2 AND lpx1=lpx2 THEN
'vertical
IF py>=MIN(lpy1,lpy2) AND py<=MAX(lpy1,lpy2) THEN RETURN px-lpx1 ELSE RETURN -1 'pos if point right else neg.
ELSE
'not horizontal
RETURN -1
ENDIF
END DEF
'==========
DEF base2base$(num$,from_base,to_base,s$)
RETURN dec2base$(base2dec(num$,from_base,s$),to_base,s$)
END DEF
'==========
DEF base2dec(num$,from_base,s$)
IF s$=""THEN s$="0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz#%"
IF LEN(s$)<from_base THEN RETURN -1
n=INSTR(s$,MID$(num$,OPTION_BASE(),1))-OPTION_BASE()
IF LEN(num$)=1 THEN
RETURN n
ELSE
RETURN n*(from_base^(LEN(num$)-1)) + base2dec(RIGHT$(num$,LEN(num$)-1),from_base,s$)
ENDIF
END DEF
'==========
DEF dec2base$(n,to_base,s$)
IF s$="" THEN s$="0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz#%"
IF LEN(s$)<to_base THEN RETURN -1
IF n<to_base THEN
RETURN MID$(s$,n+OPTION_BASE(),1)
ELSE
RETURN dec2base$(FLOOR(n/to_base),to_base, s$) & MID$(s$,(n%to_base)+OPTION_BASE(),1)
ENDIF
END DEF
'==========
'=============includemaths-end=========
, here my modest first contribution to the library.
