###### tags: `3D` `js`
# CSG (Constructive Solid Geometry) note
# type
----
# vector
:::spoiler 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
```javascript
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
```javascript
this-(this-a)*t
```
## len
## unit
單位為1的向量
## cross
降階值
```javascript
[[x ,y ,z ],
[a.x,a.y ,a.z]]
```
:::
# vertex
:::spoiler 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
:::spoiler 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
:::spoiler 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
:::spoiler 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
```javascript
+-------+ +-------+
| | | |
| A | | |
| +--+----+ = | +
+----+--+ | +----+
| B |
| |
+-------+
```
## allPolygons
return combon all polygon from back and front to one array
:::
----
# Boolean operations
:::spoiler Boolean operations
## union
```javascript
a.clipTo(b);
b.clipTo(a);
b.invert();
b.clipTo(a);
b.invert();
a.build(b.allPolygons());
```
my way
```javascript
a.clipTo(b);
b.clipTo(a);
a.build(b.allPolygons());
```
## subtract
```javascript
a.invert();
a.clipTo(b);
b.clipTo(a);
b.invert();
b.clipTo(a);
b.invert();
a.build(b.allPolygons());
a.invert();
```
my way
```javascript
a.invert();
a.clipTo(b);
b.invert();
b.clipTo(a);
a.invert();
a.build(b.allPolygons());
```
## intersect
```javascript
a.invert();
b.clipTo(a);
b.invert();
a.clipTo(b);
b.clipTo(a);
a.build(b.allPolygons());
a.invert();
```
my may
```javascript
a.invert();
b.clipTo(a);
b.invert();
a.clipTo(b);
a.build(b.allPolygons());
a.invert();
```
:::
## link
[other way](http://groups.csail.mit.edu/graphics/classes/6.837/F98/talecture/)
[paper link](https://static1.squarespace.com/static/51bb9790e4b0510af19ea9c4/t/51bf7c34e4b0a897bf550945/1371503668974/CSG_report.pdf)
[github](https://github.com/x06lan/three_face_boolean)
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