Vector dot product calculation - i need help

[Unseen Machine]

Hi Folks,

As we know math is not my strong suit! I am working on my Quake 3 BSP loader (levels) and have hit a snag. All the examples i got to work from are in C++ and have their own methods of calculating the dot product. I'd rather not have to use GLM (glm::dot function) so i am hoping someone can help me out.

So i need to calculate the distance between the camera and the given vertices.

Code: QB64: [Select]

1. TYPE Vector3
2.   X AS SINGLE
3.   Y AS SINGLE
4.   Z AS SINGLE
5. END TYPE
6.  
7.  
8. DIM Cam AS Vector3, Vertices AS Vector3
9.  
10.  
11. DP = DotProduct(Cam, Vertices)
12.  
13.  
14.  
15.  
16. FUNCTION DotProduct% (Vec1 AS Vector3, Vec2 AS Vector3)
17.  
18.  
19.  
20. END FUNCTION
21.  
22.  

Thanks folks,

Unseen

[luke]

Standard dot product calculation is

Code: [Select]

FUNCTION DotProduct! (Vec1 AS Vector3, Vec2 AS Vector3)
    DotProduct! = Vec1.X * Vec2.X + Vec1.Y * Vec2.Y + Vec1.Z * Vec2.Z
END FUNCTION
I'm not sure what you mean exactly by distance - Euclidean distance in 3D between two points is sqrt((x2-x1)^2 + (y2-y1)^2 + (z2 - z1)^2) but you don't need a dot product to work that out.

[Unseen Machine]

I'm not sure what you mean exactly by distance - Euclidean distance in 3D between two points is sqrt((x2-x1)^2 + (y2-y1)^2 + (z2 - z1)^2) but you don't need a dot product to work that out.

Im not wuite sure either! I'm working from this....

const float distance = glm::dot(plane.normal, glm::vec3(pos)) - plane.distance;

and the glm thingy said

Returns the dot product of x and y, i.e., result = x * y.

So i think what youve hooked me up with should do the trick but i've got so much to do on this before i can see a result!

Thanks @luke

Unseen

[bplus]

Here are my notes from STx paper introducing vectors, some functions are written in terms of others so you might need the whole group:

Code: QB64: [Select]

1. OPTION _EXPLICIT
2. _TITLE "Vector Math" ' B+ started 2019-10-20
3. ' Based on notes provided to QB64 forum by William F Barnes, on 2019-10-19
4. ' https://www.qb64.org/forum/index.php?topic=1782.0
5. ' A vector's dimension is the number of components it has.
6. ' Here is code for processing 2 and 3 dimension vectors.
7.  
8. TYPE xyType
9.     x AS SINGLE
10.     y AS SINGLE
11. END TYPE
12.  
13. TYPE xyzType
14.     x AS SINGLE
15.     y AS SINGLE
16.     z AS SINGLE
17. END TYPE
18.  
19. ' notation 0 w/arrowHat  (no way of telling if 2, 3 or more dimensions)
20. DIM SHARED v2zero AS xyType, v3zero AS xyzType
21. v2zero.x = 0: v2zero.y = 0
22. v3zero.x = 0: v3zero.y = 0: v3zero.z = 0
23.  
24. 'Basis Vectors, isolate components e sub x Dot V w/arrowHat = V sub x
25. DIM SHARED v2e(1 TO 2) AS xyType, v3e(1 TO 3) AS xyzType
26. v2e(1).x = 1: v2e(1).y = 0
27. v2e(2).x = 0: v2e(2).y = 1
28. v3e(1).x = 1: v3e(1).y = 0: v3e(1).z = 0
29. v3e(2).x = 0: v3e(2).y = 1: v3e(2).z = 0
30. v3e(3).x = 0: v3e(3).y = 0: v3e(3).z = 1
31.  
32.  
33. '==================================================================================== test area
34.  
35. 'define a test vector
36. DIM Test AS xyzType, A AS xyzType, B AS xyzType, Inv AS xyzType, sing AS SINGLE
37. A.x = 1: A.y = 2: A.z = 3
38. B.x = -10: B.y = -20: B.z = -30
39. PRINT "A w/arrowHat = " + v3$(A)
40. PRINT "B w/arrowHat = " + v3$(B)
41. v3Add A, B, Test
42. PRINT "A + B = " + v3$(Test)
43. v3Subtr A, B, Test
44. PRINT "A - B = " + v3(Test)
45. v3Scale 10, A, Test
46. PRINT "10A = " + v3$(Test)
47. v3Inverse A, Inv
48. PRINT "A Inverse = " + v3$(Inv)
49. v3Add A, Inv, Test
50. PRINT "Check Inverse: A v3Add Inv = " + v3$(Test)
51. PRINT "A's magnitude is "; v3Magnitude(A)
52. v3Unit A, Test
53. PRINT "A's unit vector is "; v3$(Test)
54. 'isolate y component of test
55. Test.x = 10: Test.y = -101.11: Test.z = 22.37
56. DIM yComponent
57. PRINT "Test = " + v3$(Test)
58. yComponent = v3DotProduct(v3e(2), Test)
59. PRINT "Test isolate component y = v3DotProduct(v3e(2), Test) = " + ts$(yComponent) 'yeah it worked!"
60. setV3 1, 0, 0, A
61. setV3 0, 1, 0, B
62. v3CrossProduct A, B, Test
63. PRINT "A = " + v3$(A)
64. PRINT "B = " + v3$(B)
65. PRINT "A Cross B = " + v3$(Test) ' = [0, 0, 1] ?
66.  
67.  
68. '================================================= subs and fuctions
69. SUB setV3 (x, y, z, setMe AS xyzType)
70.     setMe.x = x: setMe.y = y: setMe.z = z
71. END SUB
72.  
73. FUNCTION v3$ (showMeInnards AS xyzType)
74.     v3$ = "[" + ts$(showMeInnards.x) + ", " + ts$(showMeInnards.y) + ", " + ts$(showMeInnards.z) + "]"
75. END FUNCTION
76.  
77. FUNCTION ts$ (number)
78.     ts$ = _TRIM$(STR$(number))
79. END FUNCTION
80.  
81. 'notation UppercaseLetter w/arrowhat + uppercase Letter w/arrowHat
82. SUB v2Add (A AS xyType, B AS xyType, Sum AS xyType)
83.     Sum.x = A.x + B.x
84.     Sum.y = A.y + B.y
85. END SUB
86. SUB v3Add (A AS xyzType, B AS xyzType, Sum AS xyzType)
87.     Sum.x = A.x + B.x
88.     Sum.y = A.y + B.y
89.     Sum.z = A.z + B.z
90. END SUB
91.  
92. 'notation UppercaseLetter w/arrowHat - UppercaseLetter w/arrowHat
93. SUB v2Subtr (A AS xyType, B AS xyType, Sum AS xyType)
94.     Sum.x = A.x - B.x
95.     Sum.y = A.y - B.y
96. END SUB
97. SUB v3Subtr (A AS xyzType, B AS xyzType, Sum AS xyzType)
98.     Sum.x = A.x - B.x
99.     Sum.y = A.y - B.y
100.     Sum.z = A.z - B.z
101. END SUB
102.  
103. 'notation lowercaseletter (for a number next to (times)) UppercaseLetter w/arrowHat
104. SUB v2Scale (mult AS SINGLE, A AS xyType, Scale AS xyType) 'parallels
105.     Scale.x = mult * A.x
106.     Scale.y = mult * A.y
107. END SUB
108. SUB v3Scale (mult AS SINGLE, A AS xyzType, Scale AS xyzType) 'parallels
109.     Scale.x = mult * A.x
110.     Scale.y = mult * A.y
111.     Scale.z = mult * A.z
112. END SUB
113.  
114. 'notation the inverse of A w/arrowHat is -A w/arrowHat
115. SUB v2Inverse (A AS xyType, Inverse AS xyType) ' A + InverseOfA = 0
116.     Inverse.x = -A.x
117.     Inverse.y = -A.y
118. END SUB
119. SUB v3Inverse (A AS xyzType, Inverse AS xyzType) ' A + InverseOfA = 0
120.     Inverse.x = -A.x
121.     Inverse.y = -A.y
122.     Inverse.z = -A.z
123. END SUB
124.  
125. 'notation: A w/arrowHat Dot B w/arrowHat v2 Dot Product is a number, v3 Dot Product is a vector
126. FUNCTION v2DotProduct (A AS xyType, B AS xyType) 'shadow or projection  if A Dot B = 0 then A , B are perpendicular
127.     v2DotProduct = A.x * B.x + A.y * B.y
128. END SUB
129. FUNCTION v3DotProduct (A AS xyzType, B AS xyzType) 'shadow or projection  if A Dot B = 0 then A , B are perpendicular
130.     v3DotProduct = A.x * B.x + A.y * B.y + A.z * B.z
131. END SUB
132.  
133. 'notation absolute value bars about A w/arrowHat OR just an UppercaseLetter (with no hat), its just a number
134. FUNCTION v2Magnitude (A AS xyType) 'hypotenuse of right triangle
135.     v2Magnitude = SQR(v2DotProduct(A, A))
136. END FUNCTION
137. FUNCTION v3Magnitude (A AS xyzType) 'hypotenuse of cube
138.     v3Magnitude = SQR(v3DotProduct(A, A))
139. END FUNCTION
140.  
141. 'notation: A w/arrowHat X B w/arrowHat, X is a Cross get it?
142. FUNCTION v2CrossProduct (A AS xyType, B AS xyType) ' a vector perpendicular to both A and B, v2 is a magnitude
143.     v2CrossProduct = A.x * B.y - A.y * B.x
144. END FUNCTION
145. SUB v3CrossProduct (A AS xyzType, B AS xyzType, Cross AS xyzType) ' v3 cross product is a 3d vector perpendicular to A and B
146.     'notice x has no x components, y no y componets, z no z components
147.     Cross.x = A.y * B.z - A.z * B.y
148.     Cross.y = A.z * B.x - A.x * B.z
149.     Cross.z = A.x * B.y - A.y * B.x
150. END FUNCTION
151.  
152. 'notation: A w/caratHat = A w/arrowHat divided by A (UppercaseLetter) or scaled by 1/A magnitude (no hats)
153. SUB v2Unit (A AS xyType, Unit AS xyType)
154.     DIM m AS SINGLE
155.     m = v2Magnitude(A)
156.     v2Scale 1 / m, A, Unit
157. END SUB
158. SUB v3Unit (A AS xyzType, Unit AS xyzType)
159.     DIM m AS SINGLE
160.     m = v3Magnitude(A)
161.     v3Scale 1 / m, A, Unit
162. END SUB
163.  

Doesn't look too bad (math wise):

Code: QB64: [Select]

1. FUNCTION v3DotProduct (A AS xyzType, B AS xyzType) 'shadow or projection  if A Dot B = 0 then A , B are perpendicular
2.     v3DotProduct = A.x * B.x + A.y * B.y + A.z * B.z
3. END SUB
4.