During the past decades the use of programming as a design approach has widen the architect’s creative perception and has set a new dynamic equilibrium between digital and physical space models. Frequently this newly acquired programmatic freedom leads to a wide spectrum of geometrically challenging double curved surfaces. The problem then lies on defining these objects in terms of constructible components.

Various custom tessellation algorithms have thus been developed in response to the problem mentioned above. Most of them are based on a top-down method of mapping triangular grids on the generated surface. This thesis will try to investigate whether it is possible to create a more efficient, quadrilateral tessellation algorithm by using a bottom-up approach. The hypothesis rests on the fact that by having agents estimating the curvature along the surface by making very small, fixed steps, one can have a better approximation of it, as the agents will not overstep any curve inflections. As there is no standard solution to this problem, the method will be tested against two other algorithms more commonly used to solve tessellation problems. The first is the traditional gradient descent algorithm, where the agent’s step size varies based on iterative estimations of the optimal deviation measured from the curved surface. The second emulates an original top-down approach to the problem, where the surface is defined topologically in advance and is solved globally.

Eventually, the results of this comparison show how the ‘walking agent’ method is in some ways advantageous against the other two, while capable of producing interesting tessellation patterns. Ultimately the usefulness of this new tool rests on the fact that the surface is explored based on its local curvature conditions without having to specify the mesh’s node topology in advance. Furthermore the surface is tessellated with respect to a predefined acceptable deviation threshold and maximum tile size.

[ CODE EXCERPT ]

//set the basis functions in u-direction, based on the mathematical formula

//u defines the current u-coordinate, k the control point d the degree of the b-spline //surface in u

float basisnU(float u, int k, int d) {

if (d == 0) {

return basis0U(u,k);

}

else {

float b1 = basisnU(u,k,d-1) * (u - knotsU[k]) / (knotsU[k+d] - knotsU[k]);

float b2 = basisnU(u,k+1,d-1) * (knotsU[k+d+1] - u) / (knotsU[k+d+1] - knotsU[k+1]);

return b1 + b2;

}

}

float basis0U(float u, int k){

if (u >= knotsU[k] && u < knotsU[k+1]){// && knotsU[k]

return 1;

}

else{

return 0;

}

}

//set the basis functions in v-direction, based on the mathematical formula

//u defines the current v-coordinate, m the control points and d the degree of the b-spline

//surface in v

float basisnV(float v, int m, int d) {

if (d == 0) {

return basis0V(v,m);

}

else {

float b1 = basisnV(v, m, d-1) * (v - knotsV[m]) / (knotsV[m+d] - knotsV[m]);

float b2 = basisnV(v,m+1,d-1) * (knotsV[m+d+1] - v) / (knotsV[m+d+1] - knotsV[m+1]);

return b1 + b2;

}

}

float basis0V(float v, int m){

if (v >= knotsV[m] && v < knotsV[m+1]){//&& knotsV[m]

return 1;

}

else{

return 0;

}

}

In order to accomplish this, first an emulation of the sun’s path was created. Using sliders one could then regulate the trajectory of the sun in regards 1) to the seasons and 2) to a day’s circle. The membranes’ component takes as an input the positioning of the sun in the sky sphere and adjusts itself accordingly. Eventually the component was applied to a semi-hypaethral pavilion. The renderings of various sun-studies revealed a playful variety of shadow and light patterns inside the pavilion. The sun sensitive skin transforms differently on the surface of the structure, based on the sun’s location, thus making some components to close and others to open.

component (wmv video, 0.3 Mb) - day & year trajectories (Flash video, 1.7 Mb) skin (wmv video, 1.4 Mb)

This project was created in Bentley’s Generative Components (Microstation platform). Renderings made in Microstation.

]]> http://martha.pnoe.net/blog/sun-sensitive-skin-generative-components/feed/ http://martha.pnoe.net/blog/sonic-projections/ http://martha.pnoe.net/blog/sonic-projections/#comments Mon, 15 May 2006 09:25:15 +0000 Martha Architecture http://martha.pnoe.net/blog/sonic-projections/ Sonic Projections interactive demo
(.jar file, Java needed, 0.3 Mb)

Sonic Projections (Flash presentation, 1 Mb), is an installation for the central axes that lead to Bath’s museum. The original scope of this case study is to create an inviting element towards the museum.

A generative structure & an interactive installation that explores the creation of a new Dynamic Space.

A responsive environment that not only interacts with people when triggered, but also seeks interaction. The representation of this reaction comes with the form of attractors and repulsors that travel through the installation -as humans move- and change the shape of its shell. This installation can be realized by using SmartDust technology & Ubiquitous Computing techniques.

Unfortunatelly no music with this file (no dancing arches!) but I think you will enjoy it more if it doesn’t take an hour to download it!!!

Space Embedded Network

In the case of Sonic Projections, SmartDust particles are set on the nodes of the mesh and also travel through the installation. Via TinyOS (open-source operating system designed for wireless embedded sensor networks) they transmit signals to one another and thus create a wireless peer-to-peer network. The particles travel based on swarm logic programming. In that sense, the whole network has self-organization properties and creates an intelligent space. When a traveling particle is triggered, it activates a reaction among the other swarming particles and together they act as attractors and repulsors for the mesh-connected particles, thus changing its formation.
The form emerges through a series of interactions between the humans and the particles and reality is blurred while the INTERFACE is consisted by space, architectural forms, individuals and SmartDust particles.
(Smart dust devices are tiny wireless microelectromechanical sensors -MEMS- that can detect everything, from light to vibrations. These “motes” could eventually be the size of a grain of sand, though each would contain sensors, computing circuits, bidirectional wireless communications technology and a power supply. When clustered together, they automatically create highly flexible, low-power networks.)

Mesh’s Movement
(flash movie, 1.3 Mb)

Not all Sound Patterns trigger the particles. They choose what they consider “interesting” sounds - based on sound frequencies- and follow them. In that way, a new pattern of interaction is established, where people will be challenged to find ways to attract the particles, in order to participate to the installation’s transformation. When no people pass through the installation, a certain memory mechanism recalls recorded sounds from people who were previously there and tries to create new sound patterns (testing the results through a GA) from them, in order to attract more people… a new kind of Siren in search of her Ulysses…

Arches’ Movement
(flash movie, 1.1 Mb)

The arches are generated via the script and are being transformed dynamically. This dynamic transformation is based either on input frequencies taken by a musical piece embedded in the code (dancing arches) or on the user’s interaction with the installation.

Transfomation
(flash movie, 1.6 Mb)

A rendered visualizaton of the installation, in the road that leads to Bath’s Museum.

Particle Movement
(flash movie, 0.43 Mb)

Vortices and Dynamic Space
The SmartDust particles create an embedded network inside the installation. Human emitted Sound Patterns trigger the particles which gather around him/her. The particle network tries to keep an equilibrium by keeping minimum distances from the humans, as well as from each other. In that way, patterns emerge not only on the mesh (by forces of attraction and repulsion), but also on the way particles move. The system’s self organizes itself in such a way so that the particles create toruses and vortices. The louder the Sound Patterns, the more particles participate in the “pattern creation” game.

Astroidal Variation
A variation of this installation can be created if we replace the particles on the mesh’s nodes, with an “astroidal” component. The behaviour of the installation remains the same, while the formal outcome is completelly different.

This project was created with Processing programming language. All images produced through scripting. Rendered images were exported as DXF files and rendered in CAD application.

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