CSG (Constructive Solid Geometry) note

tags: 3D js

CSG is a methodology for constructing geometries by mesh, using algorithms capable of performing boolean operations like union or difference (A-B), among others.

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

value

pos( vector)

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

value

normal 面的髮線

w

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

valuemagnitude

vertices(lot of vertex)

shared

plane

EPSILON(對於點是否在面上的容忍值)

clone

flip

flip vertex

flip plane

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

plane

front=node

back=node

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

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();

another way to intersect

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

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

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

something