SummerDay/PerspectiveTransform.gd

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GDScript3
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2021-11-18 17:23:37 +01:00
extends CSGCylinder
# Called when the node enters the scene tree for the first time.
func _ready():
g2dp_as_basis_test()
#--- UNIT TESTS ---
func g2dp_as_basis_test():
# Origin.
var o1 = Vector2(-1.0, -1.0)
var o2 = Vector2(1.0, -1.0)
var o3 = Vector2(-1.0, 1.0)
var o4 = Vector2(1.0, 1.0)
# Destination.
var d1 = Vector2(-1.0, -1.0)
var d2 = Vector2(1.0, -2.0)
var d3 = Vector2(-1.0, 1.0)
var d4 = Vector2(1.0, 1.0)
print(str(d1) + "\n" + str(d2) + "\n" + str(d3) + "\n" + str(d4) + "\n")
var m = g2dp_as_basis(o1, o2, o3, o4, d1, d2, d3, d4)
print(str(m) + "\n")
var p1 = multiply_basis_vector2(m, o1)
var p2 = multiply_basis_vector2(m, o2)
var p3 = multiply_basis_vector2(m, o3)
var p4 = multiply_basis_vector2(m, o4)
print(str(p1) + "\n" + str(p2) + "\n" + str(p3) + "\n" + str(p4) + "\n")
func multmm_test():
var m = Basis(
Vector3(5, 3, 1) ,
Vector3(0, -4, -2) ,
Vector3(0, 0, 1)
)
var mi = m.inverse()
var ma = [
m[0][0], m[0][1], m[0][2],
m[1][0], m[1][1], m[1][2],
m[2][0], m[2][1], m[2][2]
]
var mia = [
mi[0][0], mi[0][1], mi[0][2],
mi[1][0], mi[1][1], mi[1][2],
mi[2][0], mi[2][1], mi[2][2]
]
var res = multmm(ma, mia)
print(res)
#--- HELPER FUNCTIONS ---
func adj(m):
var adj = [
m[4]*m[8]-m[5]*m[7], m[2]*m[7]-m[1]*m[8], m[1]*m[5]-m[2]*m[4],
m[5]*m[6]-m[3]*m[8], m[0]*m[8]-m[2]*m[6], m[2]*m[3]-m[0]*m[5],
m[3]*m[7]-m[4]*m[6], m[1]*m[6]-m[0]*m[7], m[0]*m[4]-m[1]*m[3]
]
print("\n" + "adjunctive: " + str(adj) + "\n")
return adj
func multmm(a, b): # Multiply two matrices.
var c = range(9)
for i in range(3):
for j in range(3):
var cij = 0
for k in range(3):
cij += a[3*i + k] * b[3*k + j]
c[3*i + j] = cij
return c
func multmv(m, v): # Multiply matrix and vector.
return [
m[0]*v[0] + m[1]*v[1] + m[2]*v[2],
m[3]*v[0] + m[4]*v[1] + m[5]*v[2],
m[6]*v[0] + m[7]*v[1] + m[8]*v[2]
]
func basis_to_points(x1, y1, x2, y2, x3, y3, x4, y4):
var m = [
x1, x2, x3,
y1, y2, y3,
1.0, 1.0, 1.0
]
var v = multmv(adj(m), [x4, y4, 1.0]);
print("coeffs: " + str(v))
var b = multmm(m, [
v[0], 0.0, 0.0,
0.0, v[1], 0.0,
0.0, 0.0, v[2]
])
print("matrix: " + str(b))
return b
func general_2d_projection(
x1s, y1s, x1d, y1d,
x2s, y2s, x2d, y2d,
x3s, y3s, x3d, y3d,
x4s, y4s, x4d, y4d
):
var s = basis_to_points(x1s, y1s, x2s, y2s, x3s, y3s, x4s, y4s)
var d = basis_to_points(x1d, y1d, x2d, y2d, x3d, y3d, x4d, y4d)
var m = multmm(d, adj(s))
for i in range(9):
m[i] /= m[8]
return m
func g2dp_as_basis(
s1, s2, s3, s4,
d1, d2, d3, d4
):
var m = general_2d_projection(
s1.x, s1.y, d1.x, d1.y,
s2.x, s2.y, d2.x, d2.y,
s3.x, s3.y, d3.x, d3.y,
s4.x, s4.y, d4.x, d4.y
)
return Basis(
Vector3(m[0], m[1], m[2]),
Vector3(m[3], m[4], m[5]),
Vector3(m[6], m[7], m[8])
)
func multiply_basis_vector2(b, v):
var h = b.xform(Vector3(v.x, v.y, 1.0))
return Vector2(h.x / h.z, h.y / h.z)