Перемещение точек в 3D пространстве

у самой камеры в свойствах есть только LookDirection и UpDirection

Это по сути все, что нужно для решения задачи. Искомый вектор ортогонален обоим этим векторам, а значит является их векторным произведением - результат нужно лишь умножить на значение, зависящее от направления и величины желаемого перемещения (отрицательное для перемещения влево). Вот демонстрация перемещения влево и вправо по нажатию клавиш-стрелок:

XAML:

<Window x:Class="Wpf3d.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        Title="MainWindow" Height="350" Width="525"
         WindowState="Maximized" KeyDown="Window_KeyDown" >
    <Grid HorizontalAlignment="Stretch" VerticalAlignment="Stretch"
          >
        <Viewport3D Name="myViewport" HorizontalAlignment="Stretch"
                    VerticalAlignment="Stretch">
            <!-- Add a camera. -->
            <Viewport3D.Camera>
                <PerspectiveCamera 
                        FarPlaneDistance="20" 
                        LookDirection="0,0,1" 
                        UpDirection="0,1,0" 
                        NearPlaneDistance="1" 
                        Position="0,0,-6" 
                        FieldOfView="45" />
            </Viewport3D.Camera>
            <!-- Add models. -->
            <Viewport3D.Children>
                <ModelVisual3D>
                    <ModelVisual3D.Content>
                        <Model3DGroup >
                            <Model3DGroup.Children>
                                <!-- Lights, MeshGeometry3D and DiffuseMaterial objects are added to the ModelVisual3D. -->
                                <DirectionalLight Color="#FFFFFFFF" Direction="3,-4,5" />
                                <!-- Define a red cone. -->
                                <GeometryModel3D>
                                    <GeometryModel3D.Geometry>

                                        <MeshGeometry3D 
    Positions="0.293893 -0.5 0.404509  0.475528 -0.5 0.154509  0 0.5 0  0.475528 -0.5 0.154509  0 0.5 0  0 0.5 0  0.475528 -0.5 0.154509  0.475528 -0.5 -0.154509  0 0.5 0  0.475528 -0.5 -0.154509  0 0.5 0  0 0.5 0  0.475528 -0.5 -0.154509  0.293893 -0.5 -0.404509  0 0.5 0  0.293893 -0.5 -0.404509  0 0.5 0  0 0.5 0  0.293893 -0.5 -0.404509  0 -0.5 -0.5  0 0.5 0  0 -0.5 -0.5  0 0.5 0  0 0.5 0  0 -0.5 -0.5  -0.293893 -0.5 -0.404509  0 0.5 0  -0.293893 -0.5 -0.404509  0 0.5 0  0 0.5 0  -0.293893 -0.5 -0.404509  -0.475528 -0.5 -0.154509  0 0.5 0  -0.475528 -0.5 -0.154509  0 0.5 0  0 0.5 0  -0.475528 -0.5 -0.154509  -0.475528 -0.5 0.154509  0 0.5 0  -0.475528 -0.5 0.154509  0 0.5 0  0 0.5 0  -0.475528 -0.5 0.154509  -0.293892 -0.5 0.404509  0 0.5 0  -0.293892 -0.5 0.404509  0 0.5 0  0 0.5 0  -0.293892 -0.5 0.404509  0 -0.5 0.5  0 0.5 0  0 -0.5 0.5  0 0.5 0  0 0.5 0  0 -0.5 0.5  0.293893 -0.5 0.404509  0 0.5 0  0.293893 -0.5 0.404509  0 0.5 0  0 0.5 0  " 
    Normals="0.7236065,0.4472139,0.5257313  0.2763934,0.4472138,0.8506507  0.5308242,0.4294462,0.7306172  0.2763934,0.4472138,0.8506507  0,0.4294458,0.9030925  0.5308242,0.4294462,0.7306172  0.2763934,0.4472138,0.8506507  -0.2763934,0.4472138,0.8506507  0,0.4294458,0.9030925  -0.2763934,0.4472138,0.8506507  -0.5308242,0.4294462,0.7306172  0,0.4294458,0.9030925  -0.2763934,0.4472138,0.8506507  -0.7236065,0.4472139,0.5257313  -0.5308242,0.4294462,0.7306172  -0.7236065,0.4472139,0.5257313  -0.858892,0.429446,0.279071  -0.5308242,0.4294462,0.7306172  -0.7236065,0.4472139,0.5257313  -0.8944269,0.4472139,0  -0.858892,0.429446,0.279071  -0.8944269,0.4472139,0  -0.858892,0.429446,-0.279071  -0.858892,0.429446,0.279071  -0.8944269,0.4472139,0  -0.7236065,0.4472139,-0.5257313  -0.858892,0.429446,-0.279071  -0.7236065,0.4472139,-0.5257313  -0.5308242,0.4294462,-0.7306172  -0.858892,0.429446,-0.279071  -0.7236065,0.4472139,-0.5257313  -0.2763934,0.4472138,-0.8506507  -0.5308242,0.4294462,-0.7306172  -0.2763934,0.4472138,-0.8506507  0,0.4294458,-0.9030925  -0.5308242,0.4294462,-0.7306172  -0.2763934,0.4472138,-0.8506507  0.2763934,0.4472138,-0.8506507  0,0.4294458,-0.9030925  0.2763934,0.4472138,-0.8506507  0.5308249,0.4294459,-0.7306169  0,0.4294458,-0.9030925  0.2763934,0.4472138,-0.8506507  0.7236068,0.4472141,-0.5257306  0.5308249,0.4294459,-0.7306169  0.7236068,0.4472141,-0.5257306  0.8588922,0.4294461,-0.27907  0.5308249,0.4294459,-0.7306169  0.7236068,0.4472141,-0.5257306  0.8944269,0.4472139,0  0.8588922,0.4294461,-0.27907  0.8944269,0.4472139,0  0.858892,0.429446,0.279071  0.8588922,0.4294461,-0.27907  0.8944269,0.4472139,0  0.7236065,0.4472139,0.5257313  0.858892,0.429446,0.279071  0.7236065,0.4472139,0.5257313  0.5308242,0.4294462,0.7306172  0.858892,0.429446,0.279071  "                   TriangleIndices="0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 " />
                                    </GeometryModel3D.Geometry>
                                    <GeometryModel3D.Material>
                                        <DiffuseMaterial>
                                            <DiffuseMaterial.Brush>
                                                <SolidColorBrush 
                            Color="Red" 
                            Opacity="1.0"/>
                                            </DiffuseMaterial.Brush>
                                        </DiffuseMaterial>
                                    </GeometryModel3D.Material>
                                </GeometryModel3D>
                            </Model3DGroup.Children>
                        </Model3DGroup>
                    </ModelVisual3D.Content>
                </ModelVisual3D>
            </Viewport3D.Children>
        </Viewport3D>
    </Grid>
</Window>

C#:

using System;
using System.Collections.Generic;
using System.Text;
using System.Windows;
using System.Windows.Controls;
using System.Windows.Input;
using System.Windows.Media.Media3D;
namespace Wpf3d
{
    public partial class MainWindow : Window
    {
        PerspectiveCamera cam;
        public MainWindow()
        {
            InitializeComponent();
            cam = myViewport.Camera as PerspectiveCamera;
        }  
        private void Window_KeyDown(object sender, KeyEventArgs e)
        {
            double factor = 0.0;
            if (e.Key == Key.Left) factor = -1.0;
            else if (e.Key == Key.Right) factor = 1.0;
            else return;
            Point3D p0 = cam.Position;
            Vector3D L = cam.LookDirection;
            Vector3D U = cam.UpDirection;
            Vector3D normal = Vector3D.CrossProduct(L, U);
            normal.Normalize();
            normal = Vector3D.Multiply(factor, normal);            
            Point3D p = p0 + normal;            
            cam.Position = p;
        }
    }
}