I have following code snippet:
val tiles = for {
x <- 0 to bitmap.length by tileSize
y <- 0 to bitmap(0).length by tileSize
} yield new Tile[Number](x, y, tileSize, tileSize,
data = for {tx <- x to x + tileSize - 1;
ty <- y to y + tileSize - 1
} yield (bitmap(tx)(ty)))
This can look complicated, but the idea behind is to create Tile objects for every XY position in 3-dimensional bitmap object. The 'nested' yield that is given as a data parameter into the Tile's constructor is an IndexedSeq[Number], which should be converted to an Array[Number] to match the type of the data parameter. The problem is that toArray method doesn't exist for the final yielded object:
val tiles = for {
x <- 0 to bitmap.length by tileSize
y <- 0 to bitmap(0).length by tileSize
} yield new Tile[Number](x, y, tileSize, tileSize,
data = for {tx <- x to x + tileSize - 1;
ty <- y to y + tileSize - 1
} yield (bitmap(tx)(ty).toArray))
causes an error Cannot resolve symbol toArray, even though yield (bitmap(tx)(ty).toArray)) is shown as IndexedSeq[java.lang.Number] in IntelliJIDEA and theoretically should contain a definition of toArray method.
What is happening in the last yield? How can I convert resulting collection to an Array? I know, this code may and should be rewritten in simplier and more readable manner, but now I want to know, what is going on behind the curtain.
You need to call toArray to the final result of all the for, not to each yield.
You may do this:
val tiles = for {
x <- 0 to bitmap.length by tileSize
y <- 0 to bitmap(0).length by tileSize
} yield new Tile[Number](x, y, tileSize, tileSize,
data = (for {tx <- x to x + tileSize - 1;
ty <- y to y + tileSize - 1
} yield bitmap(tx)(ty)).toArray
However, this syntax is not encouraged in Scala, consider this snippet instead.
val tiles = for {
x <- 0 to bitmap.length by tileSize
y <- 0 to bitmap(0).length by tileSize
data = for {
tx <- x to x + tileSize - 1
ty <- y to y + tileSize - 1
} yield bitmap(tx)(ty)
tile = new Tile[Number](x, y, tileSize, tileSize, data.toArray)
} yield tile
I try to slice a DenseVector based on a elementwise boolean condition on another DenseVector:
import breeze.linalg.DenseVector
val x = DenseVector(1.0,2.0,3.0)
val y = DenseVector(10.0,20,0,30.0)
// I want a new DenseVector containing all elements of y where x > 1.5
// i.e. I want DenseVector(20,0,30.0)
val newy = y(x:>1.5) // does not give a DenseVector but a SliceVector
With Python/Numpy, I would just write y[x>1.5]
Using Breeze you have to use for comprehensions for filtering DenseVectors
val y = DenseVector(10.0,20,0,30.0)
val newY = for {
v <- y
if v > 1.5
} yield v
// or to write it in one line
val newY = for (v <- y if v > 1.5) yield v
The SliceVector resulting from y(x:>1.5) is just a view on the original DenseVector. To create a new DenseVector, use
val newy = y(x:>1.5).toDenseVector
I finally got a working tile-able version of Simplex noise working after much work, but I can't seem to get it to record and display correctly when using a BufferedImage. Whenever I try to create an image, it ends up with bands or rings of black and white, instead of a smooth change of shades, which is what I'm expecting. I'm guessing there's something simple I'm not doing, but for the life of me, I can't find it.
This is my code (quite a bit of which is from Stefan Gustavson's Simplex noise implementation):
import java.awt.image.BufferedImage
import javax.imageio.ImageIO
import java.io.File
import scala.util.Random
object ImageTest {
def main(args: Array[String]): Unit = {
val image = generate(1024, 1024, 1)
ImageIO.write(image, "png", new File("heightmap.png"))
}
def generate(width: Int, height: Int, octaves: Int) = {
val map = new BufferedImage(width, height, BufferedImage.TYPE_USHORT_GRAY)
val pi2 = Math.PI * 2
for ( x <- 0 until width;
y <- 0 until height) {
var total = 0.0
for (oct <- 1 to octaves) {
val scale = (1 - 1/Math.pow(2, oct))
val s = x / width.toDouble
val t = y / height.toDouble
val dx = 1-scale
val dy = 1-scale
val nx = scale + Math.cos(s*pi2) * dx
val ny = scale + Math.cos(t*pi2) * dy
val nz = scale + Math.sin(s*pi2) * dx
val nw = scale + Math.sin(t*pi2) * dy
total += (((noise(nx,ny,nz,nw)+1)/2)) * Math.pow(0.5, oct)
}
map.setRGB(x,y, (total * 0xffffff).toInt)
}
map
}
// Simplex 4D noise generator
// returns -1.0 <-> 1.0
def noise(x: Double, y: Double, z: Double, w: Double) = {
// Skew the (x,y,z,w) space to determine which cell of 24 simplices we're in
val s = (x + y + z + w) * F4; // Factor for 4D skewing
val i = Math.floor(x+s).toInt
val j = Math.floor(y+s).toInt
val k = Math.floor(z+s).toInt
val l = Math.floor(w+s).toInt
val t = (i+j+k+l) * G4 // Factor for 4D unskewing
val xBase = x - (i-t) // Unskew the cell space and set the x, y, z, w
val yBase = y - (j-t) //distances from the cell origin
val zBase = z - (k-t)
val wBase = w - (l-t)
// For the 4D case, the simplex is a 4D shape I won't even try to describe.
// To find out which of the 24 possible simplices we're in, we need to
// determine the magnitude ordering of x0, y0, z0 and w0.
// Six pair-wise comparisons are performed between each possible pair
// of the four coordinates, and the results are used to rank the numbers.
var rankx = 0
var ranky = 0
var rankz = 0
var rankw = 0
if(xBase > yBase) rankx+=1 else ranky+=1
if(xBase > zBase) rankx+=1 else rankz+=1
if(xBase > wBase) rankx+=1 else rankw+=1
if(yBase > zBase) ranky+=1 else rankz+=1
if(yBase > wBase) ranky+=1 else rankw+=1
if(zBase > wBase) rankz+=1 else rankw+=1
// simplex[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some order.
// Many values of c will never occur, since e.g. x>y>z>w makes x<z, y<w and x<w
// impossible. Only the 24 indices which have non-zero entries make any sense.
// We use a thresholding to set the coordinates in turn from the largest magnitude.
// Rank 3 denotes the largest coordinate.
val i1 = if (rankx >= 3) 1 else 0
val j1 = if (ranky >= 3) 1 else 0
val k1 = if (rankz >= 3) 1 else 0
val l1 = if (rankw >= 3) 1 else 0
// Rank 2 denotes the second largest coordinate.
val i2 = if (rankx >= 2) 1 else 0
val j2 = if (ranky >= 2) 1 else 0
val k2 = if (rankz >= 2) 1 else 0
val l2 = if (rankw >= 2) 1 else 0
// Rank 1 denotes the second smallest coordinate.
val i3 = if (rankx >= 1) 1 else 0
val j3 = if (ranky >= 1) 1 else 0
val k3 = if (rankz >= 1) 1 else 0
val l3 = if (rankw >= 1) 1 else 0
// The fifth corner has all coordinate offsets = 1, so no need to compute that.
val xList = Array(xBase, xBase-i1+G4, xBase-i2+2*G4, xBase-i3+3*G4, xBase-1+4*G4)
val yList = Array(yBase, yBase-j1+G4, yBase-j2+2*G4, yBase-j3+3*G4, yBase-1+4*G4)
val zList = Array(zBase, zBase-k1+G4, zBase-k2+2*G4, zBase-k3+3*G4, zBase-1+4*G4)
val wList = Array(wBase, wBase-l1+G4, wBase-l2+2*G4, wBase-l3+3*G4, wBase-1+4*G4)
// Work out the hashed gradient indices of the five simplex corners
val ii = if (i < 0) 256 + (i % 255) else i % 255
val jj = if (j < 0) 256 + (j % 255) else j % 255
val kk = if (k < 0) 256 + (k % 255) else k % 255
val ll = if (l < 0) 256 + (l % 255) else l % 255
val gradIndices = Array(
perm(ii+perm(jj+perm(kk+perm(ll)))) % 32,
perm(ii+i1+perm(jj+j1+perm(kk+k1+perm(ll+l1)))) % 32,
perm(ii+i2+perm(jj+j2+perm(kk+k2+perm(ll+l2)))) % 32,
perm(ii+i3+perm(jj+j3+perm(kk+k3+perm(ll+l3)))) % 32,
perm(ii+1+perm(jj+1+perm(kk+1+perm(ll+1)))) % 32)
// Calculate the contribution from the five corners
var total = 0.0
for (dim <- 0 until 5) {
val (x,y,z,w) = (xList(dim), yList(dim), zList(dim), wList(dim))
var t = 0.5 - x*x - y*y - z*z - w*w
total += {
if (t < 0) 0.0
else {
t *= t
val g = grad4(gradIndices(dim))
t * t * ((g.x*x)+(g.y*y)+(g.z*z)+(g.w*w))
}
}
}
// Sum up and scale the result to cover the range [-1,1]
27.0 * total
}
case class Grad(x: Double, y: Double, z: Double, w: Double = 0.0)
private lazy val grad4 = Array(
Grad(0,1,1,1), Grad(0,1,1,-1), Grad(0,1,-1,1), Grad(0,1,-1,-1),
Grad(0,-1,1,1),Grad(0,-1,1,-1),Grad(0,-1,-1,1),Grad(0,-1,-1,-1),
Grad(1,0,1,1), Grad(1,0,1,-1), Grad(1,0,-1,1), Grad(1,0,-1,-1),
Grad(-1,0,1,1),Grad(-1,0,1,-1),Grad(-1,0,-1,1),Grad(-1,0,-1,-1),
Grad(1,1,0,1), Grad(1,1,0,-1), Grad(1,-1,0,1), Grad(1,-1,0,-1),
Grad(-1,1,0,1),Grad(-1,1,0,-1),Grad(-1,-1,0,1),Grad(-1,-1,0,-1),
Grad(1,1,1,0), Grad(1,1,-1,0), Grad(1,-1,1,0), Grad(1,-1,-1,0),
Grad(-1,1,1,0),Grad(-1,1,-1,0),Grad(-1,-1,1,0),Grad(-1,-1,-1,0))
private lazy val perm = new Array[Short](512)
for(i <- 0 until perm.length)
perm(i) = Random.nextInt(256).toShort
private lazy val F4 = (Math.sqrt(5.0) - 1.0) / 4.0
private lazy val G4 = (5.0 - Math.sqrt(5.0)) / 20.0
}
I've checked the output values of the noise function I'm using, which as of yet hasn't returned anything outside of (-1, 1) exclusive. And for a single octave, the value I'm supplying to the image (total) has not gone outside of (0,1) exclusive, either.
The only thing I can see that would be a problem is either the BufferedImage type is set incorrectly, or I'm multiplying total by the wrong hex value when setting the values in the image.
I've looked through the Javadocs on BufferedImage for information about the types and the values they accept, though nothing I've found seems to be out of place in my code (though, I am fairly new to using BufferedImage in general). And I've tried changing the hex value, but neither seems to change anything. The only thing I've found that has any affect is if I divide the (total * 0xffffff).toInt value by 256, which seems to darken the bands a bit and a slight gradient appears over the areas it should, but if I increase the division too much, the image just becomes black. So as of right now I'm stuck on what could be the issue.
(total * 0xffffff).toInt doesn't seem to make sense. You are creating an ARGB value from a grayscale float with a single multiplication?
I think you want something like this:
val i = (total * 0xFF).toInt
val rgb = 0xFF000000 | (i << 16) | (i << 8) | i
That gives me a smooth random texture, although with very low contrast—with 1 octave, your total seems to vary approx from 0.2 to 0.3, so you may need to adjust the scale a bit.
I'm not sure though how you can get 16-bit grayscale resolution. Perhaps you need to set the raster data directly instead of using setRGB (which forces you down to 8 bits). The comments below this question suggest that you use the raster directly.
How to solve a linear system of matrices in scala breeze? ie, I have Ax = b, where A is a matrix (usually positive definite), and x and b are vectors.
I can see that there is a cholesky decomposition available, but I couldn't seem to find a solver? (if it was matlab I could do x = b \ A. If it was scipy I could do x = A.solve(b) )
Apparently, it is quite simple in fact, and built into scala-breeze as an operator:
x = A \ b
It doesnt use Cholesky, it uses LU decomposition, which is I think about half as fast, but they are both O(n^3), so comparable.
Well, I wrote my own solver in the end. I'm not sure if this is the optimal way to do it, but it doesn't seem unreasonable? :
// Copyright Hugh Perkins 2012
// You can use this under the terms of the Apache Public License 2.0
// http://www.apache.org/licenses/LICENSE-2.0
package root
import breeze.linalg._
object Solver {
// solve Ax = b, for x, where A = choleskyMatrix * choleskyMatrix.t
// choleskyMatrix should be lower triangular
def solve( choleskyMatrix: DenseMatrix[Double], b: DenseVector[Double] ) : DenseVector[Double] = {
val C = choleskyMatrix
val size = C.rows
if( C.rows != C.cols ) {
// throw exception or something
}
if( b.length != size ) {
// throw exception or something
}
// first we solve C * y = b
// (then we will solve C.t * x = y)
val y = DenseVector.zeros[Double](size)
// now we just work our way down from the top of the lower triangular matrix
for( i <- 0 until size ) {
var sum = 0.
for( j <- 0 until i ) {
sum += C(i,j) * y(j)
}
y(i) = ( b(i) - sum ) / C(i,i)
}
// now calculate x
val x = DenseVector.zeros[Double](size)
val Ct = C.t
// work up from bottom this time
for( i <- size -1 to 0 by -1 ) {
var sum = 0.
for( j <- i + 1 until size ) {
sum += Ct(i,j) * x(j)
}
x(i) = ( y(i) - sum ) / Ct(i,i)
}
x
}
}