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Разделы > Геометрия > задача:


51041 - Plane Segmentation

Задачи раздела

• 50237 - Is it the same color?
• 50668 - Triangle
• 50664 - Polygons
• 50263 - Points
• 50268 - Triangles
• 50663 - Lights
• 50670 - Picture
• 51041 - Plane Segmentation
• 50422 - Area and Perimeter of diffe...
• 50473 - Counting Circles Positions
• 50327 - Parallel Lines
• 50362 - Pythagorean Numbers
• 50328 - How far away
• 50397 - The Number of Points in a ...
• 50399 - Mobile Base Station
• 50487 - Radius of Inscribed Circle

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Лимит времени 2000/4000/4000/4000 мс. Лимит памяти 65000/65000/65000/65000 Кб.
bfs.

Plane Segmentation

Question: 

The plane equation in three dimensional space can be defined as:

ax + by +cz + d=0

Where a, b and c are plane parameters and d is distance of plane from the origin.

A point lies on plane if  ax + by +cz + d=0

Write a program which counts how many of this points lie on the plane.

Input Specifications: In the first line you will be given 4 coefficients of the plane (a, b, c, d) than in the following three lines x, y, z coordinates of four points. where -20000<=a,b,c<=20000, -18000000<=d<=18000000, and -100<=x,y,z<=100 .

Output Specifications: Show how many points lie on the plane.

 

Sample Input I  
-4 2 3 -3
2 2 1
2 0 3
3 2 5
Sample Input II
2 2 2 -18
1 2 6
5 1 5
3 2 4
Sample Output I
0
Sample Output II
2

 

Sample Input II Explanation:

Based on plane equation we check if the points lie on plane or not.

Check Point 1

equation= ax + by +cz + d=1*2 + 2*2 + 2*6 + (-18)=2+4+12-18=0

Check Point 2

equation= ax + by +cz + d=2*5 + 2*1 + 2*5 + (-18)=10+2+5-18=4

Check Point 2

equation= ax + by +cz + d=2*3 + 2*2 + 2*4 + (-18)=6+4+8-18=0

Total number of points lying on plane is 2

 
 
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