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created at **Mode Lab Experiments**

R-trees are balanced tree data structures used for spatial access methods in N-dimensional space. Implementing the RTree Class will allows us to reduce the search space by incorporating a searching sphere or bbox . R-tree is also a balanced search tree (so all leaf nodes are at the same height), organizes the data in pages, and is designed for storage on disk.

The key idea of the data structure is to group nearby objects and represent them with their minimum bounding rectangle (MBR) in the next higher level of the tree. Since all objects lie within this bounding rectangle, a query that does not intersect the bounding rectangle also cannot intersect any of the contained objects. At the leaf level, each rectangle describes a single object; at higher levels the aggregation of an increasing number of objects. This can also be seen as an increasingly coarse approximation of the data set. – Wikipedia

Calculation Time Comparison Between Code Versions in Seconds. Search Space Sampling 1 Million Points from 1 Point to find X nearest in a 500 unit radius then closest within that range. Searches 1 Million Points in a (5000,5000,5000) Unit Cube

RTREE Rhinocommon

- Tree Item Count = 1,000,000
- Found closest n point in 9 tests
- CALCULATION TIME TAKEN : 0.002 sec
- Search sphere size of 500

Rhinocommon Python

- Point Count = 1,000,000
- ClosestPoint = [2092.39 , 2955.144 , 2235.82]
- Number of Points in Range = 4151
- CALCULATION TIME TAKEN : 0.512 sec
- Search sphere size of 500

Rhinoscript Python

- Point Count = 1,000,000
- ClosestPoint = [2192.45 , 2958.38 , 2230.98]
- Number of Points in Range = 4236
- CALCULATION TIME TAKEN : 3.95 sec

RTREE Rhinocommon

- Tree Item Count = 1,000,000
- Number of Points in Range = 1
- CALCULATION TIME TAKEN : 0.00099 sec

Rhinocommon Python

- Point Count = 1,000,000
- Number of Points in Range = 1
- CALCULATION TIME TAKEN : 0.015 sec

Rhinoscript Python

- Point Count = 1,000,000
- Number of Points in Range = 1
- CALCULATION TIME TAKEN : 2.72 sec

RTREE Rhinocommon

- Mesh Vertex Count = 393,216
- Number of Agents = 50
- Iteration Steps = 200
- CALCULATION TIME TAKEN : 9.7 sec
- Search Radius = 4

Rhinocommon Python

- Mesh Vertex Count = 393,216
- Number of Agents = 50
- Iteration Steps = 200
- CALCULATION TIME TAKEN : 1390 sec
- Search Radius = 4

Rhinoscript Python

- Mesh Vertex Count = 393,216
- Number of Agents = 50
- Iteration Steps = 200
- CALCULATION TIME TAKEN : N/A Either Crashes or gave up because time was insanely long
- Search Radius = 4

Why the drastic difference in performance?

import Rhino import rhinoscriptsyntax as rs import scriptcontext from System.Drawing import Color import random as rnd import time """-------------------------------------------------------- PERFORMANCE TEST - RTREE CLASS RHINOCOMMON Repeated Search To Find Closest Neighbor Search Sample = 1 Million Points Search Radius = 500 Units Search Space = Cube (5000,5000,5000) --------------------------------------------------------""" class SearchData: def __init__(self, pts, point): #Search Data class set up for instancing repeaded searching and tracking self.HitCount = 0 #amount of times we searched starts with 0 self.arrPts = pts self.Point = point self.Index = -1 #insuring that we reduce the search radius after the first pass, see the conditional in searchcallback self.Distance = 0 self.count = 0 def SearchCallback(sender, e): data = e.Tag data.HitCount += 1 #incrementing the hitcount vertex = data.arrPts[e.Id] #the current closest neighbor distance = data.Point.DistanceTo(vertex) #distance to the current closest neighbor from the query loc to define new search radius if data.Index == -1 or data.Distance > distance: #condition to resize the search sphere to optimize the searching e.SearchSphere = Rhino.Geometry.Sphere(data.Point, distance) #resize the search sphere data.Index = e.Id #update the data.index to current point ID data.Distance = distance #update the data.distance to the current distance def RunSearch(): pttimeStart = time.time() #Start Timer point = Rhino.Geometry.Point3d(5000/2,5000/2,5000/2) intNumPts = 1000000 #specify the number of sample points to search pts = [] tree = Rhino.Geometry.RTree() #create a new instance of the rtree class for x in range(0,intNumPts): randomPt = Rhino.Geometry.Point3d(rnd.random()*50000,rnd.random()*50000,rnd.random()*50000) #randomly place each point inside the 5k x 5k x 5k cube pts.append(randomPt) #add the current point to the end of the pts list tree.Insert(randomPt,x) #insert the current random point in the RTree at the specified index (x) pttimeEnd = time.time() #end the timer print "time taken to create pts: {}".format(pttimeEnd - pttimeStart) #print amount of time it took for calculations print "TreeCount = {}".format(tree.Count) #count of the amount of items in the tree timeStart = time.time() #Start Timer data = SearchData(pts, point) #Create an instance of the Search Data Class passing sample list, query loc sphere = Rhino.Geometry.Sphere(point, 500) #specify the inital search sphere size if tree.Search(sphere, SearchCallback, data): #call the search method from the Rtree Class print "Found point in {0} tests".format(data.HitCount) #print the amount of search iterations we did print "ClosestPt = {}".format(data.arrPts[data.Index]) #print the closest neighbor timeEnd = time.time() #end the timer print "time taken: {}".format(timeEnd - timeStart) #print amount of time it took for calculations if __name__=="__main__": RunSearch() Update

import Rhino import rhinoscriptsyntax as rs import scriptcontext from System.Drawing import Color import random as rnd import time """-------------------------------------------------------- RHINOCOMMON METHODS One Time Search to find all points within specified radius The points found inside the specified radius get sampled for closest neighbor No Repeat Search Search Sample = 1 Million Points Search Radius = 500 Units Search Space = Cube (5000,5000,5000) --------------------------------------------------------""" def closestSearch(pts, point): #function to sample point based on a search radius first then search for the closest inside that list mimic the rtree pass basically but with brute force ptsinRange = [] #dynamic list to store points found inside initial search for i, pt in enumerate(pts): dist = point.DistanceTo(pt) #find the distance from each point to the query point if dist < 500: ptsinRange.append(pt) #if the distance is less than 500 append that point to the ptsinRange List cPoint = Rhino.Collections.Point3dList.ClosestPointInList(ptsinRange,point) #search for the closest point from that list of points in range if cPoint[0] == point[0] and cPoint[1] == point[1] and cPoint[2] == point[1]: #test against the closest neighbor being you print "IS THE SAME" return cPoint,ptsinRange #return the closest neighbor and the list of points in range def RunSearch(): point = Rhino.Geometry.Point3d(5000/2,5000/2,5000/2) intNumPts = 1000000 #specify number of sample points pts = [] #store the random points in an empty list for x in range(0,intNumPts): randomPt = Rhino.Geometry.Point3d(rnd.random()*5000,rnd.random()*5000,rnd.random()*5000) #randomly place each point inside the 5k x 5k x 5k cube pts.append(randomPt) #append each random point to the pts list timeStart = time.time() #Start timer data = closestSearch(pts, point) #call closestsearch function Pass query pt and list of points to search print "ClosestPoint = {}".format(data[0]) #print the closest neighbor print "Number of Pts in Range = {}".format(len(data[1])) #print how many points were captures inside the search radius timeEnd = time.time() #stop the timer print "time taken: {}".format(timeEnd - timeStart) #print the amount of time the calculations took if __name__=="__main__": RunSearch() Update

import Rhino import rhinoscriptsyntax as rs import scriptcontext from System.Drawing import Color import random as rnd import time """-------------------------------------------------------- RHINOSCRIPT METHODS USING PYTHON One Time Search to find all points within specified radius The points found inside the specified radius get sampled for closest neighbor No Repeat Search Search Sample = 1 Million Points Search Radius = 500 Units Search Space = Cube (5000,5000,5000) --------------------------------------------------------""" def closestSearch(pts, point): #function to sample point based on a search radius first then search for the closest inside that list mimic the rtree pass basically but with brute force ptsinRange = []#dynamic list to store points found inside initial search for i in range(len(pts)): dist = rs.Distance(pts[i],point)#find the distance from each point to the query point if dist < 500: ptsinRange.append(pts[i])#if the distance is less than 500 append that point to the ptsinRange List cPointIndex = rs.PointArrayClosestPoint(ptsinRange,point)#search for the closest index from that list of points in range cPoint = ptsinRange[cPointIndex] #find the closest point in the in range list from the index found above if cPoint[0] == point[0] and cPoint[1] == point[1] and cPoint[2] == point[1]:#test against the closest neighbor being you print "IS THE SAME" return cPoint,ptsinRange #return the closest neighbor and the list of points in range def main(): point = [5000/2,5000/2,5000/2] intNumPts = 1000000#specify number of sample points pts = []#store the random points in an empty list for x in range(0,intNumPts): randomPt = [rnd.random()*5000,rnd.random()*5000,rnd.random()*5000] #randomly place each point inside the 5k x 5k x 5k cube pts.append(randomPt)#append each random point to the pts list timeStart = time.time()#Start timer data = closestSearch(pts, point)#call closestsearch function Pass query pt and list of points to search print "ClosestPoint = {}".format(data[0])#print the closest neighbor print "Number of Pts in Range = {}".format(len(data[1]))#print how many points were captures inside the search radius timeEnd = time.time()#stop the timer print "time taken: {}".format(timeEnd - timeStart)#print the amount of time the calculations took main() Update

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