Node: Applying Transforms to Points Intro, Next: , Previous: Transforms, Up: Transforms

### Applying Transforms to Points

A `Transform` t is applied to a `Point` P using the binary `*=` operation (`Point::operator*=(const Transform&)`) which performs matrix multiplication of `P.transform` by `t`. See Point Reference; Operators.

```     Point P(0, 1);
Transform t;
t.rotate(90);
t.show("t:");
-| t:
1       0       0       0
0       0      -1       0
0       1       0       0
0       0       0       1
P *= t;
P.show_transform("P:");
-| P:
Transform:
1       0       0       0
0       0      -1       0
0       1       0       0
0       0       0       1
P.show("P:");
-| P: (0, 0, -1)
```

In the example above, there is no real need to use a `Transform`, since `P.rotate(90)` could have been called directly. As constructions become more complex, the power of `Transforms` becomes clear:

```     1. Point p0(0, 0, 0);
2. Point p1(10, 5, 10);
3. Point p2(16, 14, 32);
4. Point p3(25, 50, 99);
5. Point p4(12, 6, 88);
6. Transform a;
7. a.shift(2, 3, 4);
8. a.scale(1, 3, 1);
9. p2 *= p3 *= a;
10. a.rotate(p0, p1, 75);
11. p4 *= a;
12. p2.show("p2:");
-| p2: (18, 51, 36)
13. p3.show("p3:");
-| p3: (27, 159, 103)
14. p4.show("p4:");
-| p4: (24.4647, -46.2869, 81.5353)
```

In this example, a is shifted and scaled, and a is applied to both in line 9. This works, because the binary operation `operator*=(const Transform& t)` returns t, making it possible to chain invocations of `*=`. Following this, a is rotated 75 degrees

about the line through p_0 and p_1. Finally, all three transformations, which are stored in a, are applied to p_4.