## point

Points rock and roll within a predefined solution space. It should be based on a sound input of course but this is only a test to see if I can handle a timer and graph input at the same time.  I’ll modify this definition to actuate with sound.  The use of timer component gives a certain degree of randomness on the overall formation, while I start to be very discouraged with the exploratory limits of dataflow design. Here is the Grasshopper definition: [GHX:0.9.0061]. I’ve found a sound cable with small jacks on […]

This is a simple trick that shows the utilization of “surface split” component in Grasshopper. It is used to detect inner regions of any given two-dimensional linework, resembling the hatch boundary detection of AutoCAD. There is no hatch component in Grasshopper but maybe this could be used as a starting point. Here is the simple definition if you want to try: [GHX: 0.9.0056]. I used “project” component to quickly understand which of the trimmed surfaces is inside. “Point in curves” component also gives the same solution.

Today’s tip is about the two dimensional curve-point calculations. It is very handy to use “closest point” components in Grasshopper. You can calculate distances and directions between curves, surfaces and points and place point objects in relation with the proximity of another object. However there is no “farthest point” implemented yet. I tried to calculate a farthest point from a curve. First, tried to translate curve in a fashion that it would result the opposite of closest point calculation, giving the farthest point. However this idea has collapsed quickly because […]

We can create tessellations of outer points in a Poincare Disk, using the manual method explained in the last post (here). But repeating that compass and straightedge process is becoming a little useless after a couple of repeats. If you say “ok. I understood the concept, let’s get faster!” then we can model just the same process in Grasshopper3D to examine varying results in seconds; If we connect any grid of points into this definition, we can clearly see the similar result we obtained by actually projecting the hyperbolic surface on […]

Poincare disk is still an interesting representation of hyperbolic space for me, full of mysteries. I’ve had several attempts to understand it previously (here and here). Finally I found a resource* explaining basic concepts about it. I tried to repeat some of the constructions in Rhinoceros, (without any logical purpose). The most important part is the conversion of an Euclidean point into a hyperbolic space. There is no clear formula, directly projecting a point into Hyperbolic space, but the method seems very interesting to me because we can do this […]

Yesterday, Kağan asked me about what isovist component in Grasshopper is and how it works? In fact, it is a long story, I said because once upon a time, I was curious about Space Syntax theory as my old friend Ela Çil introduced it to me. Here is an original definition of Michael Benedikt; The environment is defined as a collection of visible real surfaces in space. An isovist is the set of all points visible from a given vantage point in space and with respect to an environment. The […]

Today, there are pedagogical and practical challenges on the use of algorithms in architectural design, as computer puts not only a physical but also a cognitive layer between designer and the subject. Formulation of this cognitive layer is becoming important, regarding which model of computing is used to connect designer with the subject. Is it a “designerly” search, or design exploration in a visual programming environment? As most of the researchers admit that visual programming environments are very effective in generating variations, but on the other hand, it dramatically changes the way […]

This is the basic form of a surface division, based on curvature. As each point on the surface has a curvature value, this might be used to dispatch those values and see the points at flat and curved parts of the surface. Here is the Grasshopper definition [GHX: 0.8.0066] (Please use right click + save target as to download ghx definitions in this site. Otherwise your browser may try to execute them as they are xml files). I used my favourite surface equation definition (here) as implemented equation of cos(x)+cos(y) in the animation […]

[2011_12_25_divide] here is the fundamental of surface subdivision in Grasshopper. In order to design a parametric truss exercise, this is generally accepted starting point. Get a surface from the file, subdivide it into U and V directions to create point lists and then manipulate these points to create something interesting. Having a list of points would also present good potentials regarding attraction with other entities, such as point or curve attractors. As you probably notice, this is the new version of Grasshopper, which also includes NURBS objects. As a parametric […]

Trying to create above pattern (as described in Sunflower Spiral) as simple as possible, this definition (can be downloaded here: [2011_12_24_circles] creates not only spirals, but also capable of more fundamental tessellations. Maybe a three-dimensional equivalent should be studied.

This experiment is based on a traditional surface-component definition. However, the variation of component is associated with Gaussian curvature. We just control the subdivision and a multiplier value. Results are interesting in as an educational tool to explain NURBS surface curvature and it’s utilization for Design Geometry. Different surface shapes generate exciting results. Of course this could be much improved by recognizing positive and negative curvature values, (probably only accepting positive ones maybe). Grasshopper definition can be downloaded here [2011_12_22_gauss].

Sunflower (or Fermat’s, or Phyllotaxis) spiral can be constructed in Grasshopper3D according to the Vogel’s model of parametric relationships using polar coordinates. Definition file can be downloaded here [GHX: 0.8.0066] It’s a good example of utilizing polar coordinates. It’s also fun to play with parameters and constraints, also there are very interesting results if you also connect the polar angle value to the “z” of point component

Since the “Sine Surface” has become vey popular, it’s best used in educational settings where quick and effective parametric surfaces are needed. However, I tried to further develop this idea to create not only the sine edge surface, but also a surface that can be mapped by any graph function. The definition found here [2011_12_22_sine]does calculate points according to a graph output, but does not create edge surface yet. Here is an updated version of this project Update: Here is an updated version of this Grasshopper definition: [GHX: 0.9.0072]