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tsh73
Feb 8, 2013
Title of Page
Complex numbers (a library & demonstrations) by tenochtitlanuk
uses ATAN2() function coded by Stefan Pendl (thread Collision detection maths error , reply 6)
There are times then you need add vectors, scale vectors, decompose vectors into normal and tangential parts.
In these times, this library might prove handy.
Of cource calling functions take time so everything works slower - but they say
"Make it RUN, make it run RIGHT, then make it run FAST".
Vectors are stored in a string as a space-separated pair of numbers.
So there is roundoff errors. Also, ther are no checks if length of vector is null - so function vectUnit$(v$) might fail on that.
As slight bonus, you can use vectors "as is" in graphic commands.
Like this
Vector 2d library
Closely related toComplex numbers (a library & demonstrations) by tenochtitlanuk
uses ATAN2() function coded by Stefan Pendl (thread Collision detection maths error , reply 6)
There are times then you need add vectors, scale vectors, decompose vectors into normal and tangential parts.
In these times, this library might prove handy.
Of cource calling functions take time so everything works slower - but they say
"Make it RUN, make it run RIGHT, then make it run FAST".
Vectors are stored in a string as a space-separated pair of numbers.
So there is roundoff errors. Also, ther are no checks if length of vector is null - so function vectUnit$(v$) might fail on that.
As slight bonus, you can use vectors "as is" in graphic commands.
Like this
v1$=vect$(100,100)Or even like this
v2$=vect$(300,200)
main.graphicbox1 "line ";v1$;" ";v2$
offset$=vect$(100,100)
v1$=vect$(1,1)
v2$=vect$(3,2)
main.graphicbox1 "line ";vectAdd$(offset$,vectScale$(10,v1$));" ";vectAdd$(offset$,vectScale$(10,v2$))
Console (text mode) demo
'vector 2d lib demo
'vectors stored as "x y" pairs, (to be splitted by Word$)
'by tsh73, Feb 2013
'creating a vector
v1$=vect$(3,4)
print "New vector created: ";v1$
'copying a vector. Just assign to string variable
v2$=v1$
print "Getting a components of a vector:"
print vectX(v1$)
print vectY(v1$)
print "Length of a vector:"
print vectLen(v1$)
print "Unit vector (length=1) with same direction:"
u1$=vectUnit$(v1$)
print u1$
print "and it's length is (as should be):"
print vectLen(u1$)
print "Adding vectors"
print "let's make another vector"
v3$=vect$(1,-2)
print v3$
print "The sum (";v1$;") + (";v3$;") is"
print vectAdd$(v1$,v3$)
print "Subtracting same two vectors"
print "(";v1$;") - (";v3$;") is"
print vectSub$(v1$,v3$)
print "Dot product of same two vectors"
print "(";v1$;")*(";v3$;") is"
print vectDotProduct(v1$,v3$)
print "as a side note, it is 0 for perpendicular vectors"
print "Scaling a vector"
print "by half"
print vectScale$(0.5,v1$)
print "3x"
print vectScale$(3,v1$)
print "reverse vector by multiplying it by -1"
print vectScale$(-1,v1$)
print "We can decompose any vector into sum "
print "of normal and tangential parts along any direction"
print "First, let's try along OX axis"
base$ = vect$(1,0)
print "The direction is "; base$
t$=vectTangent$(v1$,base$)
print "Tangential part is ";t$
n$=vectNorm$(v1$,base$)
print "Normal part is ";n$
print "Their sum is "; vectAdd$(t$,n$)
print "(same as initial vector)"
print "Now try it with another direction"
base$ = v3$
print "The direction is "; base$
t$=vectTangent$(v1$,base$)
print "Tangential part is ";t$
n$=vectNorm$(v1$,base$)
print "Normal part is ";n$
print "Their sum is "; vectAdd$(t$,n$)
print "(should be same as initial vector)"
print "(Well, you see there is roundoff errors possible)"
print "Angle between vector and OX axis, radians"
print vectAngle(v1$)
print "So with length and angle, we can convert to polar coords"
print "Vector ";v1$;" is"
print "Polar radius and angle "
r=vectLen(v1$)
a=vectAngle(v1$)
print r, a
print "There is a function to convert from polar to cartesian"
print vectFromPolar$(r, a)
print "(should be same as initial vector)"
print "Some other vector: length 7 at angle 60 degrees"
r=7
a=60*acs(-1)/180 'acs(-1)==pi
print vectFromPolar$(r, a)
print "Rotating vector by arbitrary agle"
print "by 30 degrees"
print vectRotate$(v1$,30*acs(-1)/180)
print "by 90 degrees"
a=90*acs(-1)/180 'acs(-1)==pi, so it's actually pi/2
print vectRotate$(v1$,a)
print "by -90 degrees"
print vectRotate$(v1$,0-a) 'JB doesn't allow "-a"
print "by 180 degrees"
print vectRotate$(v1$,180*acs(-1)/180)
print "(Well, easier to myltiply by -1)"
print "*That's all, folks.*"
end
'=================================
'vector 2d lib
'vectors as "x y" pairs, to be splitted by Word$
'by tsh73, Feb 2013
function vect$(x,y)
vect$=x;" ";y
end function
function vectX(v$)
vectX=val(word$(v$,1))
end function
function vectY(v$)
vectY=val(word$(v$,2))
end function
function vectLen(v$)
x=val(word$(v$,1))
y=val(word$(v$,2))
vectLen=sqr(x*x+y*y)
end function
function vectUnit$(v$)
x=val(word$(v$,1))
y=val(word$(v$,2))
vectLen=sqr(x*x+y*y)
vectUnit$=x/vectLen;" ";y/vectLen
end function
function vectAdd$(v1$,v2$)
x1=val(word$(v1$,1))
y1=val(word$(v1$,2))
x2=val(word$(v2$,1))
y2=val(word$(v2$,2))
vectAdd$=x1+x2;" ";y1+y2
end function
function vectSub$(v1$,v2$)
x1=val(word$(v1$,1))
y1=val(word$(v1$,2))
x2=val(word$(v2$,1))
y2=val(word$(v2$,2))
vectSub$=x1-x2;" ";y1-y2
end function
function vectDotProduct(v1$,v2$)
x1=val(word$(v1$,1))
y1=val(word$(v1$,2))
x2=val(word$(v2$,1))
y2=val(word$(v2$,2))
vectDotProduct=x1*x2+y1*y2
end function
function vectScale$(a,v$) 'a * vector v$
x=val(word$(v$,1))
y=val(word$(v$,2))
vectScale$=a*x;" ";a*y
end function
function vectTangent$(v$,base$)
n$=vectUnit$(base$)
vectTangent$=vectScale$(vectDotProduct(n$,v$),n$)
end function
function vectNorm$(v$,base$)
vectNorm$=vectSub$(v$,vectTangent$(v$,base$))
end function
function vectAngle(v$)
x=val(word$(v$,1))
y=val(word$(v$,2))
vectAngle=atan2(y,x)
end function
function vectFromPolar$(rho, phi)
vectFromPolar$=rho*cos(phi);" ";rho*sin(phi)
end function
function vectRotate$(v$,alpha)
x=val(word$(v$,1))
y=val(word$(v$,2))
rho=sqr(x*x+y*y)
phi=atan2(y,x)+alpha
vectRotate$=rho*cos(phi);" ";rho*sin(phi)
end function
function dePi$(x) 'pure aestetics
pi = acs(-1)
dePi$=x/pi;"Pi"
end function
'---------------------------
function atan2(y,x)
pi = acs(-1) 'could be made global to save some ticks
if x <> 0 then arctan = atn(y/x)
select case
case x > 0
atan2 = arctan
case y>=0 and x<0
atan2 = pi + arctan
case y<0 and x<0
atan2 = arctan - pi
case y>0 and x=0
atan2 = pi / 2
case y<0 and x=0
atan2 = pi / -2
end select
end function
Same demo but with graphics
'vector 2d lib demo
' - Graphic part
'by tsh73, Feb 2013
global offset$, scale
'window and instructions
gosub [initWindow]
call waitClick
'creating a vector
v1$=vect$(3,4)
print "New vector created: ";v1$
' drawing part
gosub [axes]
call drawVector v1$
call waitClick
'copying a vector. Just assign to string variable
v2$=v1$
print "Getting a components of a vector:"
print vectX(v1$)
print vectY(v1$)
#gr "color green"
call drawVector vect$(vectX(v1$), 0)
#gr "color blue"
call drawVector vect$(0, vectY(v1$))
call waitClick
print "Length of a vector:"
print vectLen(v1$)
print "Unit vector (length=1) with same direction:"
u1$=vectUnit$(v1$)
print u1$
print "and it's length is (as should be):"
print vectLen(u1$)
#gr "color cyan"
call drawVector u1$
call waitClick
print "Adding vectors"
print "let's make another vector"
v3$=vect$(1,-2)
print v3$
print "The sum (";v1$;") + (";v3$;") is"
print vectAdd$(v1$,v3$)
gosub [axes]
call drawVector v1$
#gr "color green"
call drawVector v3$
#gr "color blue"
call waitClick
call drawVector vectAdd$(v1$,v3$)
call waitClick
print "Subtracting same two vectors"
print "(";v1$;") - (";v3$;") is"
print vectSub$(v1$,v3$)
gosub [axes]
call drawVector v1$
#gr "color green"
call drawVector v3$
call waitClick
#gr "color blue"
call drawVector vectSub$(v1$,v3$)
call waitClick
print "Dot product of same two vectors"
print "(";v1$;")*(";v3$;") is"
print vectDotProduct(v1$,v3$)
print "as a side note, it is 0 for perpendicular vectors"
print "Scaling a vector"
print "by half"
print vectScale$(0.5,v1$)
print "3x"
print vectScale$(3,v1$)
print "reverse vector by multiplying it by -1"
print vectScale$(-1,v1$)
gosub [axes]
call drawVector v1$
#gr "color green"
#gr "size 3"
call drawVector vectScale$(0.5,v1$)
call waitClick
#gr "color blue"
#gr "size 1"
call drawVector vectScale$(3,v1$)
call waitClick
#gr "color cyan"
#gr "size 2"
call drawVector vectScale$(-1,v1$)
call waitClick
print "We can decompose any vector into sum "
print "of normal and tangential parts along any direction"
print "First, let's try along OX axis"
base$ = vect$(1,0)
print "The direction is "; base$
t$=vectTangent$(v1$,base$)
print "Tangential part is ";t$
n$=vectNorm$(v1$,base$)
print "Normal part is ";n$
print "Their sum is "; vectAdd$(t$,n$)
print "(same as initial vector)"
gosub [axes]
call drawVector v1$
#gr "size 4"
#gr "color cyan"
call drawVector base$
call waitClick
#gr "size 2"
#gr "color blue"
call drawVector t$
call waitClick
#gr "color green"
call drawVector n$
call waitClick
print "Now try it with another direction"
base$ = v3$
print "The direction is "; base$
t$=vectTangent$(v1$,base$)
print "Tangential part is ";t$
n$=vectNorm$(v1$,base$)
print "Normal part is ";n$
print "Their sum is "; vectAdd$(t$,n$)
print "(should be same as initial vector)"
print "(Well, you see there is roundoff errors possible)"
gosub [axes]
call drawVector v1$
#gr "size 4"
#gr "color cyan"
call drawVector base$
call waitClick
#gr "size 2"
#gr "color blue"
call drawVector t$
call waitClick
#gr "color green"
call drawVector n$
call waitClick
print "Angle between vector and OX axis, radians"
print vectAngle(v1$)
print "So with length and angle, we can convert to polar coords"
print "Vector ";v1$;" is"
print "Polar radius and angle "
r=vectLen(v1$)
a=vectAngle(v1$)
print r, a
print "There is a function to convert from polar to cartesian"
print vectFromPolar$(r, a)
print "(should be same as initial vector)"
print "Some other vector: length 7 at angle 60 degrees"
r=7
a=60*acs(-1)/180 'acs(-1)==pi
print vectFromPolar$(r, a)
gosub [axes]
call drawVector v1$
call waitClick
#gr "color blue"
call drawVector vectFromPolar$(r, a)
call waitClick
print "Rotating vector by arbitrary agle"
print "by 30 degrees"
print vectRotate$(v1$,30*acs(-1)/180)
print "by 90 degrees"
a=90*acs(-1)/180 'acs(-1)==pi, so it's actually pi/2
print vectRotate$(v1$,a)
print "by -90 degrees"
print vectRotate$(v1$,0-a) 'JB doesn't allow "-a"
print "by 180 degrees"
print vectRotate$(v1$,180*acs(-1)/180)
print "(Well, easier to myltiply by -1)"
gosub [axes]
call drawVector v1$
#gr "color green"
call drawVector vectRotate$(v1$,30*acs(-1)/180)
call waitClick
#gr "color blue"
call drawVector vectRotate$(v1$,a)
call waitClick
#gr "color cyan"
call drawVector vectRotate$(v1$,0-a)
call waitClick
#gr "color black"
call drawVector vectRotate$(v1$,180*acs(-1)/180)
call waitClick
#gr "place 70 200"
#gr "\";"*That's all, folks.*"
print "*That's all, folks.*"
wait
'----------------------------------------
'parts related to graphic part of the demo
[initWindow]
UpperLeftX = 1
UpperLeftY = 1
WindowWidth = 400
WindowHeight = 400
open "Vector demo" for graphics_nsb_nf as #gr
#gr "trapclose [quit]"
#gr "home; down; posxy cx cy"
'print cx, cy
offset$ = vect$(cx, cy)
scale = 20
#gr "place 70, 120"
#gr "\";"Please align this window"
#gr "\";"along with mainwin (console)."
#gr "\";"It will print stuff to mainwin, "
#gr "\";"while drawing in this window."
#gr "\";""
#gr "\";"Use left mouse button click"
#gr "\";"to advance."
return
sub waitClick
#gr "flush"
#gr "when leftButtonDown [cont]"
wait
[cont]
#gr "when leftButtonDown"
exit sub
[quit] 'and we could close while waiting
close #gr
print "*program ended, you can close this window*"
end
end sub
function fix$(v$) '"fixes" coords of vector to use on screen:
'applies scaling and offset.
'fix$ = vectAdd$(offset$, vectScale$(scale,v$))
'really simple, isn't?
'Well, almost. "Y" should be reversed
fix$=vectAdd$(offset$, vectScale$(scale, reverseY$(v$)))
end function
function reverseY$(v$)
x=val(word$(v$,1))
y=val(word$(v$,2))
reverseY$=x;" ";0-y
end function
[axes]
'axes
bounds = 7 'like, -7 .. 7
#gr "cls"
#gr "color black; size 1"
#gr "line ";fix$(vect$(-1-bounds,0));" ";fix$(vect$(1+bounds,0))
#gr "line ";fix$(vect$(0,-1-bounds));" ";fix$(vect$(0,1+bounds))
for i = 0-bounds to bounds
#gr "line ";fix$(vect$(i,-0.1));" ";fix$(vect$(i,0.1))
#gr "line ";fix$(vect$(-0.1,i));" ";fix$(vect$(0.1,i))
next
#gr "size 2"
#gr "color red" 'default first vector will be red, width 2
#gr "flush"
return
sub drawVector v$
#gr "line ";fix$(vect$(0,0));" ";fix$(v$)
end sub
[quit] close #gr
print "*program ended, you can close this window*"
end
'=================================
'vector 2d lib
'vectors as "x y" pairs, to be splitted by Word$
'by tsh73, Feb 2013
function vect$(x,y)
vect$=x;" ";y
end function
function vectX(v$)
vectX=val(word$(v$,1))
end function
function vectY(v$)
vectY=val(word$(v$,2))
end function
function vectLen(v$)
x=val(word$(v$,1))
y=val(word$(v$,2))
vectLen=sqr(x*x+y*y)
end function
function vectUnit$(v$)
x=val(word$(v$,1))
y=val(word$(v$,2))
vectLen=sqr(x*x+y*y)
vectUnit$=x/vectLen;" ";y/vectLen
end function
function vectAdd$(v1$,v2$)
x1=val(word$(v1$,1))
y1=val(word$(v1$,2))
x2=val(word$(v2$,1))
y2=val(word$(v2$,2))
vectAdd$=x1+x2;" ";y1+y2
end function
function vectSub$(v1$,v2$)
x1=val(word$(v1$,1))
y1=val(word$(v1$,2))
x2=val(word$(v2$,1))
y2=val(word$(v2$,2))
vectSub$=x1-x2;" ";y1-y2
end function
function vectDotProduct(v1$,v2$)
x1=val(word$(v1$,1))
y1=val(word$(v1$,2))
x2=val(word$(v2$,1))
y2=val(word$(v2$,2))
vectDotProduct=x1*x2+y1*y2
end function
function vectScale$(a,v$) 'a * vector v$
x=val(word$(v$,1))
y=val(word$(v$,2))
vectScale$=a*x;" ";a*y
end function
function vectTangent$(v$,base$)
n$=vectUnit$(base$)
vectTangent$=vectScale$(vectDotProduct(n$,v$),n$)
end function
function vectNorm$(v$,base$)
vectNorm$=vectSub$(v$,vectTangent$(v$,base$))
end function
function vectAngle(v$)
x=val(word$(v$,1))
y=val(word$(v$,2))
vectAngle=atan2(y,x)
end function
function vectFromPolar$(rho, phi)
vectFromPolar$=rho*cos(phi);" ";rho*sin(phi)
end function
function vectRotate$(v$,alpha)
x=val(word$(v$,1))
y=val(word$(v$,2))
rho=sqr(x*x+y*y)
phi=atan2(y,x)+alpha
vectRotate$=rho*cos(phi);" ";rho*sin(phi)
end function
function dePi$(x) 'pure aestetics
pi = acs(-1)
dePi$=x/pi;"Pi"
end function
'---------------------------
function atan2(y,x)
pi = acs(-1) 'could be made global to save some ticks
if x <> 0 then arctan = atn(y/x)
select case
case x > 0
atan2 = arctan
case y>=0 and x<0
atan2 = pi + arctan
case y<0 and x<0
atan2 = arctan - pi
case y>0 and x=0
atan2 = pi / 2
case y<0 and x=0
atan2 = pi / -2
end select
end function