amazing video by a clever canadian who has coded up a fluid simulation using particles, similar to what i’m currently working on in p5 – only that his one seems to be working ;-)
hell, yeah!
– while working on the liquids code i realized that i need LOTS more particles to generate the level of detail i found in the analog photographs i did before. so after a few days of reading hundreds of opengl tutorials, research papers, game developers articles and 20+ p5 tests i'm finally getting closer to writing a particle system that can simulate 65k - 262k particles in real-time at 60+ fps. on my laptop (!), not a specialized über-workstation – in case you wonder.
that's a drastic increase over my previous java based system that could realistically do about 2k particles (10k was pushing it - ran at about 14 fps).
ill post some details on the new system soon, when its ready ...
The german sculptor Ulrich Rückriem, well known for geometrically divided and rearranged blocks of stone, now shows a series of conceptual drawings in a small exhibit at Museum Ludwig in Cologne. The black and white wall drawing and prints are based on a grid of 7×7=49 crosspoints.
7 points are selected and connected by straight lines which touch each point only one time and then get back to their origin. This produces a variety of acute-angled geometrical drawings.
The aesthetic system is based on what is known as a standoff situation in checkers game: Eight pieces stand on positions on the game board from where none of them can beat one another, neither on horizontal or vertical lines nor on diagonals.
39 quasi-scientific paintings and drawings. Musing on the meaning of life, surrounding a twelve foot high black column filled with whirling computers. A hexagonal structure, The Thinker emits an electronic hum generated by the bank of computers inside. The computers are set to operate for 33,000 years with an LED display counting the seconds up to 76.5 years (the average human lifespan).
Tyson said it was his take on sculptor Rodin’s famous piece, The Thinker.
“The Thinker is a twelve foot high black column that houses a series of computers inside it, running an artificial life programme which has been programmed in such a way that it evolves. There is no physical manifestation of the fact that it is thinking, and I’m fascinated by the idea that when you come across it you have a thing that is thinking but which is impenetrable – that you can’t get within its skin. Once the thing sets off, I can predict that it’s thinking for about half an hour but after that I’ve got no idea – so I’m as much in the dark as everyone else as to what it’s actually thinking about.”
It is part of a series entitled “The Seven Wonders of the World”.
“That is a series of works that relate to things I find wonderous. I wanted to make works that were not illustrative of some scientific or philosophical theory but embodied it – were in fact the actual theory made manifest. The Thinker really thinks, and is thought. The fact that human beings have reached a stage where they can find a mathematical methodology for creating thought itself, and that we can comprehend our own existence, are some of the things I am trying to manifest in this work. It also relates to this idea that we can never actually prove what the internal dialogue of another human being actually is. It’s about the way in which everybody’s universe is impenetrable, and the way everyone who thinks has their own separate universe.”
the library is getting nearer to being actually useful. it now creates new collada materials and effects for you as needed without writing a line of extra code.
it’s still quite basic and only exports triangles without any material information.
however there have been major refactorings under the hood that will allow to add new features much easier.
it might output garbage when you try to do something clever but give it a go
- your comments & critics are appreciated!
libCollada allows you to easily export 3D geometry and material data in the COLLADA 1.4.1 format from your processing applications.
Although processing’s drawing methods and COLLADA’s scenegraph based, more complex 3D description format, do not match directly – the library attempts to do a reasonable conversion, requiring no extra API to learn.
For the most part, vector operations in four space are simple extensions of
their three-space counterparts. For example, computing the addition of two
four-vectors is a matter of forming a resultant vector whose components are
the sum of the pairwise coordinates of the two operand vectors. In the same
fashion, subtraction, scaling, and dot-products are all simple extensions of
their more common three-vector counterparts.
In addition, operations between four-space points and vectors are also
simple extensions of the more common three-space points and vectors. For
example, computing the four-vector difference of four-space points is a simple
matter of subtracting pairwise coordinates of the two points to yield the four
coordinates of the resulting four-vector.
For completeness, the equations of the more common four-space vector
operations follow. In these equations,
U = <U0, U1, U2, U3>
and V = <V0, V1, V2, V3>
are two source four-vectors and k is a scalar value:
U + V = <U0 + V0, U1 + V1, U2 + V2, U3 + V3>
U - V = <U0 - V0, U1 - V1, U2 - V2, U3 - V3>
kV = <kU0, kU1, kU2, kU3>
U·V = U0V0 + U1V1 + U2V2 + U3V3
Vector Cross Product
The main vector operation that does not extend trivially to four-space is
the cross product. A three-dimensional space is spanned by three basis
vectors, so the cross-product in three-space computes an orthogonal
three-vector from two linearly independent three-vectors. Hence, the
three-space cross product is a binary operation.
In N-space, the resulting vector must be orthogonal to the remaining N-1
basis vectors. Since a four-dimensional space requires four basis vectors,
the four-space cross product requires three linearly independent four-vectors
to determine the remaining orthogonal vector. Hence, the four-space cross
product is a trinary operation; it requires three operand vectors and yields a
single resultant vector. In the remainder of this paper, the four-dimensional
cross product will be represented in the form X4(U,V,W).
To find the equation of the four-dimensional cross product, we must first
establish criteria of the cross product. These are as follows:
If the operand vectors are not linearly independent, the cross product
must be the zero vector.
If the operand vectors are linearly independent, then the resultant
vector must be orthogonal to each of the operand vectors.
The four-space cross product preserves scaling, i.e. for any
scalar k:
kX4(U,V,W)
= X4(kU,V,W)
= X4(U,kV,W)
= X4(U,V,kW)
Changing the order of two of the operands results only in a sign change
of the resultant vector.
It turns out that a somewhat simple-minded approach to computing the
four-dimensional cross product is the correct one. To motivate this idea, we
first consider the three-dimensional cross product. The 3D cross product can
be thought of as the determinant of a 3x3 matrix whose entries are as
follows:
+- -+
| i j k |
X3(U,V) = | U0 U1 U2 |
| V0 V1 V2 |
+- -+
where U and V are the operand vectors, and i, j & k represent the unit components of the resultant vector. The
determinant of this matrix is
i (U1V2 - U2V1) - j (U0V2 - U2V0) + k (U0V1 - U1V0)
which is the three-dimensional cross product. Using this idea, we'll form
the analogous 4x4 matrix, and see if it meets the four cross product
properties listed above:
[2.1a]
+- -+
| i j k l |
X4(U,V,W) = | U0 U1 U2 U3 |
| V0 V1 V2 V3 |
| W0 W1 W2 W3 |
+- -+
If the operand vectors are linearly dependent, then the vector rows of the
4x4 matrix will be linearly dependent, and the determinant of this
matrix will be zero. This satisfies the first condition. The third
condition is also satisfied, since a scalar multiple of one of the vectors
yields a scalar multiple of one of the rows of the 4x4 matrix. This results
in a determinant that is scaled by that factor, so condition three is also
met.
The fourth condition falls out as a property of determinants, i.e. when two rows of a determinant matrix are interchanged, only the sign of the
determinant changes. Hence, the fourth condition is also met.
The second condition is proven by calculating the dot product of the
resultant vector with each of the operand vectors. These dot products will
be zero if and only if the resultant vector is orthogonal to each of the
operand vectors.
The dot product of the resultant vector X4(U,V,W) with the operand
vector U is the following (refer to equation [2.1b]):
which is zero, since the first two rows are identical. Hence, the resultant
vector X4(U,V,W) is orthogonal to the operand vector U. In the same way, the
dot products of V·X4(U,V,W) and W·X4(U,V,W)
are given by the determinants
Therefore, the second condition is also met, and equation [2.1a] meets all four of the criteria for the
four-dimensional cross product.
Since the calculation of the four-dimensional cross product involves
2x2 determinants that are used more than once, it is best to store these
values rather than re-calculate them. The following algorithm uses this
idea.
// Cross4 computes the four-dimensional cross product of the three vectors
// U, V and W, in that order. It returns the resulting four-vector.
Vector4 *Cross4 (Vector4 *result, Vector4 U, Vector4 V, Vector4 W)
{
double A, B, C, D, E, F; // Intermediate Values
// Calculate intermediate values.
A = (V[0] * W[1]) - (V[1] * W[0]);
B = (V[0] * W[2]) - (V[2] * W[0]);
C = (V[0] * W[3]) - (V[3] * W[0]);
D = (V[1] * W[2]) - (V[2] * W[1]);
E = (V[1] * W[3]) - (V[3] * W[1]);
F = (V[2] * W[3]) - (V[3] * W[2]);
// Calculate the result-vector components.
*result[0] = (U[1] * F) - (U[2] * E) + (U[3] * D);
*result[1] = - (U[0] * F) + (U[2] * C) - (U[3] * B);
*result[2] = (U[0] * E) - (U[1] * C) + (U[3] * A);
*result[3] = - (U[0] * D) + (U[1] * B) - (U[2] * A);
return result;
}
Source: jeffreydocherty.com
