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Luxor torus knot examples

The following brief examples demonstrate usage of the sweep-mesh and sweep-strand-mesh functions in combination with thi.ng/luxor’s test scene setup. The first example computes a Cinquefoil knot (a (5,2)-torus knot) and sweeps a circle along the path using PTF. The second demo also uses the same knot as basis, but instead of sweeping it directly, first computes N strands, each rotating around the path at given radius and each strand swept as mesh individually (then combined into a single mesh using g/into). Both examples are tangled into the /babel/examples directory, but will only work in a REPL which has both the geom and luxor libs on its classpath.

(ns thi.ng.geom.examples.types.ptf-knot
  (:require
   [thi.ng.geom.core :as g]
   [thi.ng.geom.vector :as v]
   [thi.ng.geom.aabb :as a]
   [thi.ng.geom.circle :as c]
   [thi.ng.geom.ptf :as ptf]
   [thi.ng.math.core :as m :refer [THIRD_PI TWO_PI]]
   [thi.ng.luxor.scenes :as scene]
   [thi.ng.luxor.io :as lio]))

(defn cinquefoil
  [t]
  (let [t  (* t m/TWO_PI)
        pt (* 2.0 t)
        qt (* 5.0 t)
        qc (+ 3.0 (Math/cos qt))]
    (v/vec3 (* qc (Math/cos pt)) (* qc (Math/sin pt)) (Math/sin qt))))

(-> (scene/base-scene {:width 640 :height 360})
    (scene/add-main-mesh
     (ptf/sweep-mesh
      (mapv cinquefoil (m/norm-range 400))
      (g/vertices (c/circle 0.5) 20)
      {:align? true :loop? true})
     {:id :knot :bounds (a/aabb 1.5) :target [0 0.5 -2] :rx (- m/THIRD_PI)})
    (lio/serialize-scene "ptf-knot" false)
    (lio/export-scene)
    (dorun))

Some example renders to illustrate the weave-mesh approach/function with different parameters:

(ns thi.ng.geom.examples.types.ptf-knot2
  (:require
   [thi.ng.geom.core :as g]
   [thi.ng.geom.vector :as v]
   [thi.ng.geom.aabb :as a]
   [thi.ng.geom.circle :as c]
   [thi.ng.geom.ptf :as ptf]
   [thi.ng.math.core :as m]
   [thi.ng.luxor.scenes :as scene]
   [thi.ng.luxor.io :as lio]))

(defn cinquefoil
  [t]
  (let [t  (* t m/TWO_PI)
        pt (* 2.0 t)
        qt (* 5.0 t)
        qc (+ 3.0 (Math/cos qt))]
    (v/vec3 (* qc (Math/cos pt)) (* qc (Math/sin pt)) (Math/sin qt))))

(def knot
  (-> (mapv cinquefoil (m/norm-range 400))
      (ptf/compute-frames)
      (ptf/align-frames)))

(-> (scene/base-scene {:width 640 :height 360})
    (scene/add-main-mesh
     (ptf/sweep-strand-mesh knot 0.5 10 7 (g/vertices (c/circle 0.1) 20) {:loop? true})
      ;;(ptf/sweep-strand-mesh knot 0.8 6 12 (g/vertices (c/circle 0.1) 20))
     {:id :knot-weave :bounds (a/aabb 1.5) :target [0 0.5 -2] :rx (- m/THIRD_PI)})
    (lio/serialize-scene "ptf-knot-weave" false)
    (lio/export-scene)
    (dorun))

(ns thi.ng.geom.examples.types.ptf-knot3
  (:require
   [thi.ng.geom.core :as g]
   [thi.ng.geom.vector :as v]
   [thi.ng.geom.circle :as c]
   [thi.ng.geom.ptf :as ptf]
   [thi.ng.math.core :as m]
   [thi.ng.luxor.core :as lux]
   [thi.ng.luxor.scenes :as scene]
   [thi.ng.luxor.io :as lio]
   [thi.ng.color.core :as col]))

(defn cinquefoil
  [t]
  (let [t  (* t m/TWO_PI)
        pt (* 2.0 t)
        qt (* 5.0 t)
        qc (+ 3.0 (Math/cos qt))]
    (v/vec3 (* qc (Math/cos pt)) (* qc (Math/sin pt)) (Math/sin qt))))

(defn add-meshes
  [scene meshes opts]
  (let [hue (/ 1.0 (count meshes))]
    (reduce
     (fn [scene [i mesh]]
       (let [mat (str "matte-hue-" i)]
         (-> scene
             (lux/material-matte mat {:diffuse (col/hsva (* i hue) 1.0 0.9)})
             (scene/add-mesh mesh (assoc opts :material mat :id (str "strand-" i))))))
     scene (zipmap (range) meshes))))

(def knot
  (-> (mapv cinquefoil (m/norm-range 400))
      (ptf/compute-frames)
      (ptf/align-frames)))

(-> (scene/base-scene {:width 640 :height 360})
    (add-meshes
     (ptf/sweep-strands knot 0.5 10 7 (g/vertices (c/circle 0.1) 20) {:loop? true})
     {:tx {:translate [0 0.5 -2] :scale 0.175 :rx -65}})
    (lio/serialize-scene "ptf-knot-weave-spectrum" false)
    (lio/export-scene)
    (dorun))

(ns thi.ng.geom.examples.types.ptf-spline
  (:require
   [thi.ng.geom.core :as g]
   [thi.ng.geom.vector :as v]
   [thi.ng.geom.aabb :as a]
   [thi.ng.geom.bezier :as b]
   [thi.ng.geom.circle :as c]
   [thi.ng.geom.ptf :as ptf]
   [thi.ng.math.core :as m]
   [thi.ng.luxor.core :as lux]
   [thi.ng.luxor.scenes :as scene]
   [thi.ng.luxor.io :as lio]))

(-> (scene/base-scene {:width 640 :height 360})
    (assoc-in [:camera "perspective" :focaldistance 1] 1.4)
    (scene/add-main-mesh
     (ptf/sweep-mesh
      (-> (for [i (range 100)] (v/randvec3))
          (b/auto-spline3)
          (g/vertices))
      (g/vertices (c/circle 0.025) 10))
     {:id :spline :bounds (a/aabb 1.25) :target [0 0.625 -1.75] :rx (- m/THIRD_PI)})
    (lio/serialize-scene "ptf-spline" false)
    (lio/export-scene)
    (dorun))