tags: 3D js

CSG (Constructive Solid Geometry) note

type

---

vector

vector

values

x,y,z for a point or normal

clone

return new same vector

negated

return new same negated

plus(a)

return new vector add a vector

minus(a)

this-a

times(a)

乘a

divideBy(a)

除a

dot(a)

內積

return x*a.x+y*a.y+z*a.z

lerp(a,t)

t通常小於1
用來表示this 到a 之間的某個數

this-(this-a)*t

len

unit

單位為1的向量

cross

降階值

[[x  ,y   ,z  ],
 [a.x,a.y ,a.z]]

vertex

vertex

value

1. pos( vector)
2. noraml (vector)

clone

flip

修改normal 方向

interpolate(a,t)

用lerp的方式產生一個介於this 與a 之間的pos and normal並用 t控制落點

plane

plane

value

1. normal 面的髮線
2. w
3. epsilon 可接受誤差值

clone

flip

change the side of the normal

formpoints(a,b,c)

create plane by 3 point vector
and w is plane dot with fisrt verctor(position)

splitPolygon(polygon, coplanarFront, coplanarBack, front, back)

以這個面為基準將多個面區分為語法線面相同的front 或back
如果有交集則切割面

polygon

polygon

valuemagnitude

1. vertices(lot of vertex)
2. shared
3. plane
4. EPSILON(對於點是否在面上的容忍值)

clone

flip

flip vertex
flip plane

node

node

bsp:binary space partitioning tree
利用每個面的髮線區切割空間，如果空間在髮線的背面則視為true(或是包含)

value

1. plane
2. front=node
3. back=node
4. polygons=[]

clone

invert

flip polygons
flip plane
flip back and front
and change back to front 、 change front to back

clip Polygons

clipTo(bsp)

bsp:binary space partitioning tree

a和b的 bsp tree 合併=a-b的截面

+-------+            +-------+
|       |            |       |
|   A   |            |       |
|    +--+----+   =   |       +
+----+--+    |       +----+
     |   B   | 
     |       |
     +-------+

allPolygons

return combon all polygon from back and front to one array

---

Boolean operations

Boolean operations

union

a.clipTo(b);
b.clipTo(a);
b.invert();
b.clipTo(a);
b.invert();
a.build(b.allPolygons());

my way

a.clipTo(b);
b.clipTo(a);
a.build(b.allPolygons());

subtract

a.invert();
a.clipTo(b);
b.clipTo(a);
b.invert();
b.clipTo(a);
b.invert();
a.build(b.allPolygons());
a.invert();

my way

a.invert();
a.clipTo(b);

b.invert();
b.clipTo(a);
a.invert();
a.build(b.allPolygons());

intersect

a.invert();
b.clipTo(a);
b.invert();
a.clipTo(b);
b.clipTo(a);
a.build(b.allPolygons());
a.invert();

my may

a.invert();
b.clipTo(a);

b.invert();
a.clipTo(b);

a.build(b.allPolygons());
a.invert();

link

other way
paper link
github