Recent events and past failures have forced a recollection of high school algebra including matrices, determinants, Kramer's rule, line / plane equations and their solutions et al. Below are two simple applications of the 'recollection'.

contouring tool for Maya:
A simple utility wrapper around existing Maya tools to enable 'contour' cutting. Maya's history & animation engine further enabling 'contouring' along a curve. Thanks to Fuuuuulvio Wirz for suggestion / tip. Previous attempts depending on NURBS intersection tended to clog-up the history chain, resulting in untold misery!


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tri-plane intersection node a la CATIA. supports history.
strange by product of exercise was realization that MEL's lack of support for 'double' variable type, can(?)cause loss of significant digits. In this simple application it was solved by multiplying all inputs by large numbers. c++ version doesn't seem to suffer from the same problem.


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Battersea power station and bob venturi's theories argue for / (against?) semantic/semiotic absurdities that result from 'scale-shifting'.

The term `scale-free` begins to assume a lot of significance within computation aided/driven design methodologies. It is, one believes, an important albeit controversial admission to make: that conceptual form is independent of scale, application and/or context. Detail and development on the other hand has to fully support the 'chosen' scale and context of implementation.

Presented are WIP that are to going to implemented both at furniture and building scale. Potential / envisaged work-flows include parametric Catia modeling at building scale (to enable a family of houses within monetary and effort resource) and explorations milling and thermo forming technology at furniture scale. all-in-all quite exciting at as far as personal design endeavors with the aid of computers go.

more soon....

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images: idea-sketches for a private housing layout in India.









Rhino seems to always provide a nice environment to manually work out a schema for a possible design algorithm/outline i.e it provides enough 'numerically-aided' modeling tools to be able to quickly chalk out a computational schema that can then be safely implemented even in a 'not-so-numeric' an environment such as Maya.

In this case, this small-scale manageable project chalked out in rhino, helped forge the algorithmic ideas for a larger urban project.

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videos are in real-time






Interactive Maya node: simple rayTracing exercise to calculate annual&daily direct sunExposure.

Inputs: 'recieving surfaces', 'shading' surfaces, direction/s of sun.

Node can trace back from recieving surfaces or trace forward from the sky dome.

optimizations for interactivity:(see videos)
1.use of icosahedron to span sky-dome or sampling-space rather than a regular sphere.

2. heuristic neighboring search for sampling points (i.e search for intersection rays in the neighborhood of sampling points where intersections were previously found).

to do:
1. cache data for interactively visualisation of accrued data (i.e across the day / year)

2. connect to sun angle calculator.
3. add approximate measurement units / metrics.
4. add luminance, avg cloud-cover and other evaluative/characteristic metrics.
5. chart sun-path and establish 'mapping' logics, including data-overlay on unfolded sky-dome.
6. add geometry 'correcting' / suggestive solution-space.
7. add pointCloud export for Catia-parametric model.

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images of result of collaboration with Theodore Spyropoulos of minimaforms and part of the conceptual revisiting / reintepretation of project 19 by David Green, archigram. read more on L.A.W.u.N*project#20.







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In the days of ever-growing acronyms..a personal favorite.Good 0ld Fashioned Intelligence. albeit..a rip off from simon penny: good old fashioned artificial intelligence.(sic!)

more coffee break fun with straight forward animation. only camera being 'scripted'.



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....have lines, will follow!

Image:David M. Mount and Sunil Arya;





Images from simplistic implementation of the Octree algorithm in Maya. Primarily as an exercise to understand its API and class derivation within it.

BSP
"Binary space partitioning (BSP) is a method for recursively subdividing a space into convex sets by hyperplanes. This subdivision gives rise to a representation of the scene by means of a tree data structure known as a BSP tree."

Wikipedia Accessed Aug 2007

Octree
"An octree is a tree data structure in which each internal node has up to eight children. Octrees are most often used to partition a three dimensional space by recursively subdividing it into eight octants."

wikipedia Accessed Aug 2007

Approximate Nearest Neighbour
"Computing exact nearest neighbors in dimensions much higher than 8 seems to be a very difficult task. Few methods seem to be significantly better than a brute-force computation of all distances. However, it has been shown that by computing nearest neighbors approximately, it is possible to achieve significantly faster running times (on the order of 10's to 100's) often with a relatively small actual errors. ...."

David M. Mount and Sunil Arya

Even accounting for the amateur nature of our attempt, it would appear that the above holds true in 3 dimensions as well ie. an octree algorithm provides a significant advantage over brute calculation of distances only when the point distribution is sparse, point sets are large (above 50000) and some tolerances are allowed in terms of measurement.

inspiration:image from wired magazine and article on Visualizing Viruses: click for more (c)Image: Alex Dragulescu



playtime with some openGL lines: 'visualizing fields'


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Sad comparison heightens the need to get an handle on basic openGL routines including bezier curves drawing (notice segmentation), alpha blending (notice flat alpha), lighting (notice lack of) et al. goes to prove art is not independent of technique.much to learn. end of coffee break.!

used:
glPointSize(sz);glBegin( GL_POINTS );
glBegin( GL_LINE_STRIP );glLineWidth(sz);
//glEnable ( GL_LINE_STIPPLE_PATTERN); //glLineStipple(2,0x0B25);
glColor3f();glVertex3f();

By now ancient sketch script a single NURBS with 3 dimensional components. It translates the world space coordinates of the component object into the moving-space defined by the ortho-normal vectors of the surface.




Differential_geometry_of_curves
[Accessed May 2006]
Frenet Vectors.
"A Frenet frame is a moving reference frame of n orthonormal vectors which are used to describe a curve locally at each point. It is the main tool in the differential geometric treatment of curves as it is far easier and more natural to describe local properties (e.g. curvature, torsion) in terms of a local reference system than using a global one like the Euclidean coordinates..."

Darboux_frame
[Accessed May 2006]
Darboux_frame:
surface analogue to Frenet frame on a curve

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swarms and distribution of intelligence: decentralised decision making

“That war (vietnam) also proved the self-defeating nature of centralization: the more
one tries to achieve total certainty, the greater the increase in the information flow
needed to run the operation, and therefore the more uncertain the final results. Far
from solving the problem, computers ended up compounding it by producing their
own endless streams of information.” …

De landa, M. War in the Age of Intelligent Machine, (Cambridge: MIT Press, 1990)
p. 79

self similarity and difference

Architecture as an assembly of design components implicitly suggests ‘self-similarity’ and ‘difference’ amongst the parts of the system. Particulars or aspects of this similarity and difference could be multitude. Nonetheless, our research aims to ‘appose’ and /or articulate the notion with other issues that deserve to be discussed. In recent ‘parametric’ systems of design and of codification of design for construction, this aspect of similarity and difference, have tended to be manifested in the production of ‘homeo-morphic’ geometries such as ‘adaptive (to curvature) tiling’ patterns, structural skins etc. Alternatively, there have been systems, like those in robotics , that concentrated on production of non-topological difference and on aspects of ‘family’ and ‘individual’ on the basis of ‘attributes’ such as constituent parts , specific task-capacities, transformation pathways etc.

Images and videos show attempts to combine the position & directional relations betweens 'objects in a swarm' and the morphological self-similarity of 'objects in a family', towards developing an formal language of at urban scale. This apart from more weathered concerns of architecture and urbanism including discourses on performance fitness, spatial perception and experience, socio-cultural implications etc.




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