Essential Geometry. Equations Implicit – F(x,y) = 0 Parametric – P(t) = x – Q(t) = y – 0
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Transcript of Essential Geometry. Equations Implicit – F(x,y) = 0 Parametric – P(t) = x – Q(t) = y – 0
![Page 1: Essential Geometry. Equations Implicit – F(x,y) = 0 Parametric – P(t) = x – Q(t) = y – 0](https://reader036.fdocuments.net/reader036/viewer/2022082621/5a4d1b4f7f8b9ab0599a6d37/html5/thumbnails/1.jpg)
Essential Geometry
![Page 2: Essential Geometry. Equations Implicit – F(x,y) = 0 Parametric – P(t) = x – Q(t) = y – 0](https://reader036.fdocuments.net/reader036/viewer/2022082621/5a4d1b4f7f8b9ab0599a6d37/html5/thumbnails/2.jpg)
Essential Geometry
![Page 3: Essential Geometry. Equations Implicit – F(x,y) = 0 Parametric – P(t) = x – Q(t) = y – 0](https://reader036.fdocuments.net/reader036/viewer/2022082621/5a4d1b4f7f8b9ab0599a6d37/html5/thumbnails/3.jpg)
Essential Geometry
![Page 4: Essential Geometry. Equations Implicit – F(x,y) = 0 Parametric – P(t) = x – Q(t) = y – 0](https://reader036.fdocuments.net/reader036/viewer/2022082621/5a4d1b4f7f8b9ab0599a6d37/html5/thumbnails/4.jpg)
Essential Geometry
![Page 5: Essential Geometry. Equations Implicit – F(x,y) = 0 Parametric – P(t) = x – Q(t) = y – 0](https://reader036.fdocuments.net/reader036/viewer/2022082621/5a4d1b4f7f8b9ab0599a6d37/html5/thumbnails/5.jpg)
Essential Geometry
![Page 6: Essential Geometry. Equations Implicit – F(x,y) = 0 Parametric – P(t) = x – Q(t) = y – 0](https://reader036.fdocuments.net/reader036/viewer/2022082621/5a4d1b4f7f8b9ab0599a6d37/html5/thumbnails/6.jpg)
Equations
• Implicit– F(x,y) = 0
• Parametric– P(t) = x– Q(t) = y– 0 <= t <= 1
![Page 7: Essential Geometry. Equations Implicit – F(x,y) = 0 Parametric – P(t) = x – Q(t) = y – 0](https://reader036.fdocuments.net/reader036/viewer/2022082621/5a4d1b4f7f8b9ab0599a6d37/html5/thumbnails/7.jpg)
Geometric Operations
• Scan conversion– Convert geometry into pixels– Let the graphics system do it
• Bounding box – Efficiency
• Distance from a point– Selection
• Nearest Point– Snapping
• Inside/Outside– Selection
![Page 8: Essential Geometry. Equations Implicit – F(x,y) = 0 Parametric – P(t) = x – Q(t) = y – 0](https://reader036.fdocuments.net/reader036/viewer/2022082621/5a4d1b4f7f8b9ab0599a6d37/html5/thumbnails/8.jpg)
Points and Vectors
dX
dYX,Y
![Page 9: Essential Geometry. Equations Implicit – F(x,y) = 0 Parametric – P(t) = x – Q(t) = y – 0](https://reader036.fdocuments.net/reader036/viewer/2022082621/5a4d1b4f7f8b9ab0599a6d37/html5/thumbnails/9.jpg)
Geometric Operations
![Page 10: Essential Geometry. Equations Implicit – F(x,y) = 0 Parametric – P(t) = x – Q(t) = y – 0](https://reader036.fdocuments.net/reader036/viewer/2022082621/5a4d1b4f7f8b9ab0599a6d37/html5/thumbnails/10.jpg)
Geometric OperationsTop
Left Right
Bottom
![Page 11: Essential Geometry. Equations Implicit – F(x,y) = 0 Parametric – P(t) = x – Q(t) = y – 0](https://reader036.fdocuments.net/reader036/viewer/2022082621/5a4d1b4f7f8b9ab0599a6d37/html5/thumbnails/11.jpg)
Geometric Operations
X1,Y1
X1,Y1
ImplicitParametric
![Page 12: Essential Geometry. Equations Implicit – F(x,y) = 0 Parametric – P(t) = x – Q(t) = y – 0](https://reader036.fdocuments.net/reader036/viewer/2022082621/5a4d1b4f7f8b9ab0599a6d37/html5/thumbnails/12.jpg)
Geometric Operations
Cx,CyR
ImplicitParametric
![Page 13: Essential Geometry. Equations Implicit – F(x,y) = 0 Parametric – P(t) = x – Q(t) = y – 0](https://reader036.fdocuments.net/reader036/viewer/2022082621/5a4d1b4f7f8b9ab0599a6d37/html5/thumbnails/13.jpg)
Geometric OperationsTop
Left Right
Bottom
![Page 14: Essential Geometry. Equations Implicit – F(x,y) = 0 Parametric – P(t) = x – Q(t) = y – 0](https://reader036.fdocuments.net/reader036/viewer/2022082621/5a4d1b4f7f8b9ab0599a6d37/html5/thumbnails/14.jpg)
Geometric Operations
B
Cx,CyA
ImplicitParametric