Demo Programming: the Blob
"THE BLOB"
Steven Tattersall
One of the newer-style demo effects is that of "blobs", where there are two or more amorphous shaped objects which distort when they come into proximity with one another (see the ST intro for this edition of Maggie for instance). More advanced demos, especially on the PC, have this effect in 3 dimensions, but here we'll concern ourselves with the "simple" 2D version.
PRINCIPLE OF BLOBS
The idea behind blobs is not a new one, but is quite tricky to visualise at first. The best analogy is that of clouds. Clouds are in essence just like blobs - they are made up of water vapour, and when the amount of water vapour in our cloud reaches a certain level, it becomes visible to us. Below this level there is still a certain level of water vapour, but we cannot see it.
Now imagine that another cloud comes along and merges with our first cloud. Both have their own levels of water vapour at given points. Now it is possible that there are areas in these two clouds where two water levels that were previously invisible now overlap. The water levels combine to give a new level which now becomes invisble. As the two clouds pass through one another we see a continuously-changing pattern.
Exactly the same principle is used in the code to produce blobs. At any given point we simply sum the "densities" of all the elements in our system and plot the outcome.
DEFINING BLOBS
We can define the blob by means of a "density function". When we define the blob at point (x,y) - where (x=0,y=0) is the centre of the blob - we can use a formula to define the density at that point.
The density value is each case will range from 0 to 1. A value of 0 means that at this point there will be no effect from the blob. A value of 1 is the maximum density allowed: when summing our densities, any resultant value above 1 will simply be treated as 1.
For the sake of simplicity and prettiness, we will only model our process around circular blobs. First we choose a value max_r for the maximum radius of the blob. This is the distance from the centre further than which the blob will have no effect at all.
Now we can apply our algorithm to determine the density at each point of our blob. In simple pseudocode, this is:
!------------------------------------------------------------
! x and y are the co-ordinate values given as input
LET distance = sqr ( x*x + y*y) !Calc distance from centre
IF distance > max_r THEN
LET density = 0 !Outside max_r, density=0
ELSE
LET fraction = (distance/max_r)
!Convert distance to the
!range 0 to 1
LET density = (1-fraction^2) ^ 4
!calculate density function
ENDIF
!------------------------------------------------------------
Fig 1. Simple density functionThe line "LET density = (1-fraction^2) ^ 4" is the interesting one.
Firstly, it takes the value fraction and firstly converts it to a value equal to 1 at the very centre of the blob and 0 at the edge of max_r, but the function tails off increasingly quickly as we reach the outer reaches of the blob.
Secondly, the second part of this assignment statement accentuates the tail-off of density as we reach the outside even more. This is to give a smoother effect when two or more blobs combine.
Some of you might wonder why the power used here is "^4" rather than "^2" This is because we are working in two dimensions rather than three. Without going into the maths too deeply, our model here is a two-dimensional cross-section of a 3D model, so repeating the squaring of our density function is a simple way of reducing the calculations to 2 dimensions.
USING BLOBS
The supplied code for this algorithm is written in GFA basic (BLOB1.LST). It is a simple example which uses the above code as a function - FN blob(x%,y%) - to convert orthogonal x and y into a density for two blobs at each point on the screen. It then sums these densities, caps them so the sum is less than one and plots a colour for the corresponding value.
FASTER BLOB, FASTER
There are several ways of optimizing this function for use in assembly or some other lower level language. Our function above uses the "sqr" square root function to calculate the distance from the centre of the blob. By replacing "distance" with a new variable "distance_squared" we produce a revised function:
!------------------------------------------------------------
! x and y are the co-ordinate values given as input
LET distance_squared = x*x + y*y
IF distance_squared > max_r*max_r THEN
LET density = 0 !Outside max_r, density=0
ELSE
LET fraction_squared = (distance_squared/max_r/max_r)
LET density = (1-fraction_squared) ^ 4
!calculate density function
ENDIF
!------------------------------------------------------------
Fig 2. Revised density function.This is also available in "BLOB2" to show that it gives the same result.
Note the use of "fraction_squared" as a result of the substitutions.
This is because
fraction = distance
--------
max_rbut:
distance_squared = distance.distance = distance distance
---------------- ----------------- -------- . --------
max_r . max_r max_r.max_r max_r max_r(Basic GCSE Maths, apparently)
- which is equal to "fraction" squared.
BLOBS IN ASSEMBLER
Now the function is more or less ready to be converted into assembler, since the function nearly now only uses integers. We need to now change the range of "fraction" and "fraction_squared" to get something really useable.
Here are the original lines we need to change:
LET fraction_squared = (distance_squared/max_r/max_r)
LET density = (1-fraction_squared) ^ 4fraction_squared still ranges from 0 to 1. If we make it range from, say 0 to 255 by multiplying distance_squared by 256 before we start - not unreasonable for assembler - the result in "density" will range from 0 to 256^4-1 (ie a long word value in assembler)
LET fraction_squared = 256*distance_squared/max_r/max_r)
LET density = (1-fraction_squared)^4We now have the whole function in a format useable in assembler:
!------------------------------------------------------------
! x and y are the co-ordinate values given as input
LET distance_squared = x*x + y*y
IF distance_squared > max_r*max_r THEN
LET density = 0 !Outside max_r, density=0
ELSE
LET fraction_squared = 256*distance_squared/max_r/max_r)
LET density = (1-fraction_squared)^4
!calculate density function
ENDIF
!------------------------------------------------------------
Fig 3. Assembler-useable density function.Once this is written in assembler, we can store the blob as a table and simply add two or more tables together to create animated blobs. If I have time in the coming week there will be a small ST intro to this issue of Maggie which does this in realtime.
Steven Tattersall
12/10/97
email: tat@avena.com // s.j.tattersall@cms.salford.ac.uk or write c/o Maggie Towers
Reference
- POV (Persistence of Vision) Raytracer Documentation and sourcecode. This describes a blob function in 3 dimensions only, but contains lots of handy hints. Available from http://www.povray.com and in most PD libraries.
BLOB1.LST
' BLOBTEST
' Steven Tattersall
'
' This is a short program to draw a 2 dimensional "blob"
'
' The amount of attraction at (x,y) is given by:
'
' strength * ( 1 - radius^2) ^ 4 in 2 dimensions
'
' where radius = sqr ( x^2 + Y^2 )
'
'
'
'
max_r=180 ! radius of the blobs
'
blob1x%=50
blob1y%=50
blob2x%=140
blob2y%=160
'
FOR y%=0 TO 199
FOR x%=0 TO 319
den=(FN blob(x%-blob1x%,y%-blob1y%)+FN blob(x%-blob2x%,y%-blob2y%))
den%=MIN(16*den,15)
PSET x%,y%,den%
NEXT x%
NEXT y%
END
'
FUNCTION blob(x%,y%)
' ------------------------------------------------------------
' x and y are the co-ordinate values given as input
'
LET distance=SQR(x%*x%+y%*y%) !Calc distance from centre
IF distance>max_r THEN
LET density=0 !Outside max_r, density=0
ELSE
LET fraction=(distance/max_r)
' Convert distance to the
' range 0 to 1
LET density=(1-fraction^2)^4
' calculate density function
ENDIF
' ------------------------------------------------------------
RETURN density
ENDFUNCBLOB2.LST
' BLOBTEST
' Steven Tattersall
'
' This is a short program to draw a 2 dimensional "blob"
'
' The amount of attraction at (x,y) is given by:
'
' strength * ( 1 - radius^2) ^ 4 in 2 dimensions
' where radius = sqr ( x^2 + Y^2 )
'
' version 2 - revised to show a simple optimisation
'
'
max_r=180 ! radius of the blobs
'
blob1x%=50
blob1y%=50
blob2x%=140
blob2y%=160
'
FOR y%=0 TO 199
FOR x%=0 TO 319
den=(FN blob(x%-blob1x%,y%-blob1y%)+FN blob(x%-blob2x%,y%-blob2y%))
den%=MIN(16*den,15)
PSET x%,y%,den%
NEXT x%
NEXT y%
END
'
FUNCTION blob(x%,y%)
' ------------------------------------------------------------
' x and y are the co-ordinate values given as input
LET distance_squared=x%*x%+y%*y%
IF distance_squared>max_r*max_r THEN
LET density=0 !Outside max_r, density=0
ELSE
LET fraction_squared=(distance_squared/max_r/max_r)
LET density=(1-fraction_squared)^4
' calculate density function
ENDIF
RETURN density
ENDFUNC
